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	<title>Marine Mammal Conservancy &#187; Research</title>
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		<title>METHODS FOR SALVAGING  UNDERSAMPLED ACOUSTIC DATA BY Shaun T. Perisho</title>
		<link>http://marinemammalconservancy.org/research/methods-for-salvaging-undersampled-acoustic-data-by-shaun-t-perisho</link>
		<comments>http://marinemammalconservancy.org/research/methods-for-salvaging-undersampled-acoustic-data-by-shaun-t-perisho#comments</comments>
		<pubDate>Tue, 05 Jan 2010 03:15:41 +0000</pubDate>
		<dc:creator>Bob</dc:creator>
				<category><![CDATA[Other Organizations]]></category>
		<category><![CDATA[Research]]></category>

		<guid isPermaLink="false">http://marinemammalconservancy.org/?p=3396</guid>
		<description><![CDATA[METHODS FOR SALVAGING
UNDERSAMPLED ACOUSTIC DATA




BY
Shaun T. Perisho








Physics Department
California Polytechnic State University
San Luis Obispo, California


2008
TABLE OF CON&#8230;]]></description>
			<content:encoded><![CDATA[<p align="center">METHODS FOR SALVAGING</p>
<p align="center">UNDERSAMPLED ACOUSTIC DATA</p>
<p align="center">
<p align="center">
<p align="center">
<p align="center">
<p align="center">BY</p>
<p align="center">Shaun T. Perisho</p>
<p align="center">
<p align="center">
<p align="center">
<p align="center">
<p align="center">
<p align="center">
<p align="center">
<p align="center">
<p align="center">Physics Department</p>
<p align="center">California Polytechnic State University</p>
<p align="center">San Luis Obispo, California</p>
<p align="center">
<p align="center">
<p align="center">2008</p>
<p align="center">TABLE OF CONTENTS</p>
<p>SECTION                                                                                                       PAGE</p>
<ol>
<li>Theoretical Background                                                                         1
<ol>
<li>The Nyquist Theorem and Aliasing                                                           1</li>
<li>The Fourier Transform and FFT                                                               5</li>
</ol>
</li>
<li>Simulation                                                                                           6</li>
<li>Experiment                                                                                          12
<ol>
<li>The Apparatus                                                                                     12</li>
<li>Data Collection                                                                                    13</li>
</ol>
</li>
<li>Analysis                                                                                              17</li>
<li>Conclusion                                                                                           18</li>
</ol>
<p>Appendix:</p>
<p>A. sampling.m Program Code                                                                                 19</p>
<p>B. 150Hz Matlab Excel Data                                                                                  20</p>
<p>C. 472Hz Matlab Excel Data                                                                                  21</p>
<p>D. 150Hz LoggerPro Data                                                                                      22</p>
<p>E. 472Hz LoggerPro Data                                                                                      23</p>
<p>Bibliography                                                                                                        25</p>
<p align="center">LIST OF TABLES</p>
<p>TABLE                                                                                                            PAGE</p>
<ol>
<li>Matlab Data for the 300Hz Run                                                                10 &#8211; 11</li>
<li>LoggerPro Data for the 300Hz Run                                                            16 – 17</li>
</ol>
<p align="center">
<p align="center">____________________________________________</p>
<p align="center">
<p align="center">LIST OF FIGURES</p>
<p>FIGURE                                                                                                         PAGE</p>
<ol>
<li>Signal Composed of a Single Frequency                                            4</li>
<li>Signal Observed at a Sampling Rate Below the Nyquist      Cutoff       5</li>
<li>Analog Signal Recorded in Digital Format                                        5</li>
<li>Simplest Curve That Can Be Drawn Through All Sampled      Points    6</li>
<li>Simulated 300Hz Signal                                                                     9</li>
<li>Matlab Data for the 150Hz run                                                          12</li>
<li>Matlab Data for the 300Hz run                                                          13</li>
<li>Matlab Data for the 472Hz run                                                          14</li>
<li>Experimental Setup                                                                             15</li>
<li>300 Hz LoggerPro Data                                                                      16</li>
<li>LoggerPro Data for the 150Hz Run                                                   18</li>
<li>LoggerPro Data for the 300Hz Run                                                   19</li>
<li>LoggerPro Data for the 472Hz Run                                                   19</li>
</ol>
<p align="center">Methods for Salvaging Undersampled Acoustic Data</p>
<p align="center">By Shaun Perisho</p>
<p align="center">
<p align="center">A common problem that arises when dealing with high-frequency signal processing is aliasing due to undersampling. When sampling a signal, any frequency component it may contain over the Nyquist frequency cutoff (a number that depends on the sampling rate) can be “aliased” to a lower frequency. For example, when sampling at 50 kHz, an 80 kHz signal would appear in the Fast Fourier Transform (FFT) as a 20 kHz signal. This project aims to look at the FFTs of undersampled frequencies both in a Matlab simulation and in a controlled experiment and find a relationship between actual and aliased frequencies. Our ultimate goal is to explore applications of these findings to real world signal processing, specifically marine biology research.</p>
<p align="center">
<p><strong>I. THEORETICAL BACKGROUND</strong></p>
<p>A. The Nyquist Theorem and Aliasing</p>
<p>The conversion of an audio signal from analog to digital involves sampling the original (continuous) sound wave at regular intervals. The amplitude of this original wave is recorded at each interval and these values make up a discrete, digital representation of the original wave. The initial sound is stored as a set of numbers. When we want to listen to the recording, this set of numbers is used to rebuild the original signal and is ultimately sent through speakers to our ears.</p>
<p>The Nyquist Theorem states that as long as the sampling frequency is over twice that of the original signal, no information is lost and the sound can be reconstructed accurately<sup>1</sup>. One of the challenges inherent in working with marine mammal recordings is that they often contain frequencies that are much higher than most sound recording devices are built for and as a result, information can be lost. For data taken at a sampling rate of 50 kHz, the Nyquist Theorem states that nothing can be known about frequencies above 50/2 = 25 kHz. On top of that, frequencies above this inherent cutoff point (called the Nyquist frequency) can muddy the data as a whole, manifesting themselves falsely as lower frequency signals (a phenomenon known as aliasing).</p>
<p>In general, this loss of higher frequency information and aliasing is unavoidable. It’s not related to shortcomings in the software or the mathematical algorithms used to analyze the data – the only way to remedy it is to increase the sampling rate, meaning data recorded at insufficient sampling rates is forever limited. However, in reviewing the Nyquist proofs it seems that there may be a way to combine the observed aliasing patterns with information about the sampling rate to get a rough estimate of what the original sound wave looked like.</p>
<p>The theorem is best understood through an example. Imagine a sound composed of a single high frequency (figure 1).</p>
<p align="center">
<p align="center">Figure 1: Original signal composed of a single frequency.</p>
<p>When this signal is observed with a digital recording device, it is sampled at regular intervals (shown in red):</p>
<p align="center">
<p align="center">Figure 2: Signal observed at a sampling rate below the Nyquist cutoff.</p>
<p>If the sampling rate is less that twice the frequency of the original signal (like that shown in figure 2), the Nyquist Theorem predicts that information will be lost. To see what is meant by “lost information” we’ll look at the discrete set of points seen by the digital recorder:</p>
<p align="center">Figure 3: The analog signal recorded in digital format.</p>
<p>When the signal is reconstructed for playback or analysis, the computer essentially “connects the dots” to recreate an analog signal.</p>
<p>Figure 4: The simplest curve that can be drawn through all sampled points.</p>
<p>Comparing this reconstructed wave to the original signal (figure 1), it’s clear that an error has been made somewhere. The reconstructed wave is of a lower frequency and longer wavelength. This phenomenon is referred to as aliasing<sup>2</sup>. Running aliased data through a signal analysis program such as Raven or Logger Pro will show sound has been detected at this lower reconstructed frequency (when it hasn’t) and nothing existed at the higher original frequency. The data is false. This has serious implications for the reliability of high frequency research findings. Due to further complications false data may appear above the Nyquist cutoff point as well &#8211; claims previously made about recordings in these ranges would be extremely questionable.</p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p>B. The Fourier Transform and FFT:</p>
<p>The algorithm that allows us to take a signal like the one mentioned above and break it into its component frequencies is called the Fourier Transform.</p>
<p align="center">
<p align="center">Equation 1: The Fourier Transform</p>
<p align="center">
<p>Where F(n) is the function in the frequency (n) domain, and f(t) is the function in the time (t) domain<sup>4</sup>. This equation takes a function, typically in the time domain, and transforms it into a function in the frequency domain. So functions as we commonly know them (in the time domain) which consist of multiple frequencies can be broken down into their component frequencies via this transform.</p>
<p>Because of the sheer magnitude of the computations involved, many fourier transforms are difficult (if not impossible) to do by hand. The Discrete Fourier Transform (DFT) allows the (continuous) fourier transform to be put into a discrete, digital, computer-friendly format. It is given in Figure 6 below:</p>
<p align="center">Equation 2: The Discrete Fourier Transform</p>
<p>The most notable differences between equations 1 and 2 is the replacement of the integral sign with a summation sign – the DFT requires the input of discrete values, where the original Fourier transform required continuous integration<sup>4</sup>.</p>
<p>A particularly efficient way of computing the DFT is the Fast Fourier Transform (FFT)<sup>5</sup>.  This is the particular algorithm used in our research. Both Matlab and LoggerPro have built-in FFT programs that we used to obtain our data.</p>
<p><strong> </strong></p>
<p><strong>II. SIMULATION</strong></p>
<p>Our first step was to model analog signals in Matlab. We wrote a program in which signals could be constructed (single or multiple frequency signals) and then sampled at adjustable rates. This program, called sampling.m, can be found in the appendix. By defining the original signal at a sufficiently high number of points and sampling it at a sufficiently low rate, we were able to create an accurate model of analog-to-digital undersampling and aliasing. We then took our constructed signals and sampled them at very low rates (typically somewhere around 100 samples per second), increasing the number of samples for each run until the Nyquist cutoff was reached and we were out of the realm of aliasing.</p>
<p>We then performed a FFT and took note of the aliased frequencies that resulted. An example is shown below:</p>
<p align="center">Figure 5: A simulated 300Hz signal sampled at 336Hz in Matlab</p>
<p>The FFT shows a signal of 36 Hz aliased from the original 300 Hz signal. The 300Hz result on the right hand side of the FFT diagram is (although accurate) a mathematical byproduct of the FFT algorithm used by Matlab and is typically thrown out by signal analysis programs, like Raven, as it refers to a frequency above the Nyquist cutoff for the 336Hz sampling rate and therefore cannot theoretically be trusted.</p>
<p>After each run, we recorded the data in an Excel spreadsheet so we could easily compare the results.</p>
<table border="0" cellspacing="0" cellpadding="0" width="541">
<tbody>
<tr>
<td width="156" valign="bottom">
<p align="center">Sampling Rate   (Hz)</p>
</td>
<td width="187" valign="bottom">
<p align="center">Matlab FFT   Results (Hz)</p>
</td>
<td width="199" valign="bottom">Actual   Frequency (300Hz)</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">41</p>
</td>
<td width="187" valign="bottom">
<p align="center">13</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">45</p>
</td>
<td width="187" valign="bottom">
<p align="center">15</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">49</p>
</td>
<td width="187" valign="bottom">
<p align="center">6</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">51</p>
</td>
<td width="187" valign="bottom">
<p align="center">6</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">55</p>
</td>
<td width="187" valign="bottom">
<p align="center">26</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">60</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">65</p>
</td>
<td width="187" valign="bottom">
<p align="center">25</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">70</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">75</p>
</td>
<td width="187" valign="bottom">
<p align="center">25</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">80</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">85</p>
</td>
<td width="187" valign="bottom">
<p align="center">40</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">90</p>
</td>
<td width="187" valign="bottom">
<p align="center">30</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">95</p>
</td>
<td width="187" valign="bottom">
<p align="center">15</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">99</p>
</td>
<td width="187" valign="bottom">
<p align="center">3</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">101</p>
</td>
<td width="187" valign="bottom">
<p align="center">3</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">120</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">121</p>
</td>
<td width="187" valign="bottom">
<p align="center">60</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">122</p>
</td>
<td width="187" valign="bottom">
<p align="center">56</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">123</p>
</td>
<td width="187" valign="bottom">
<p align="center">54</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">124</p>
</td>
<td width="187" valign="bottom">
<p align="center">52</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">125</p>
</td>
<td width="187" valign="bottom">
<p align="center">50</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">127</p>
</td>
<td width="187" valign="bottom">
<p align="center">46</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">130</p>
</td>
<td width="187" valign="bottom">
<p align="center">40</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">132</p>
</td>
<td width="187" valign="bottom">
<p align="center">36</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">134</p>
</td>
<td width="187" valign="bottom">
<p align="center">32</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">140</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">160</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">165</p>
</td>
<td width="187" valign="bottom">
<p align="center">30</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">170</p>
</td>
<td width="187" valign="bottom">
<p align="center">40</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">173</p>
</td>
<td width="187" valign="bottom">
<p align="center">46</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">175</p>
</td>
<td width="187" valign="bottom">
<p align="center">50</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">177</p>
</td>
<td width="187" valign="bottom">
<p align="center">55</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">180</p>
</td>
<td width="187" valign="bottom">
<p align="center">60</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">185</p>
</td>
<td width="187" valign="bottom">
<p align="center">70</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">190</p>
</td>
<td width="187" valign="bottom">
<p align="center">80</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">195</p>
</td>
<td width="187" valign="bottom">
<p align="center">90</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">202</p>
</td>
<td width="187" valign="bottom">
<p align="center">99</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">217</p>
</td>
<td width="187" valign="bottom">
<p align="center">83</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">222</p>
</td>
<td width="187" valign="bottom">
<p align="center">80</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">240</p>
</td>
<td width="187" valign="bottom">
<p align="center">60</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">257</p>
</td>
<td width="187" valign="bottom">
<p align="center">43</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">260</p>
</td>
<td width="187" valign="bottom">
<p align="center">40</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">280</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">305</p>
</td>
<td width="187" valign="bottom">
<p align="center">5</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">320</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">336</p>
</td>
<td width="187" valign="bottom">
<p align="center">36</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">340</p>
</td>
<td width="187" valign="bottom">
<p align="center">40</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">360</p>
</td>
<td width="187" valign="bottom">
<p align="center">60</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">380</p>
</td>
<td width="187" valign="bottom">
<p align="center">80</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">382</p>
</td>
<td width="187" valign="bottom">
<p align="center">82</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">400</p>
</td>
<td width="187" valign="bottom">
<p align="center">100</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">416</p>
</td>
<td width="187" valign="bottom">
<p align="center">116</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">420</p>
</td>
<td width="187" valign="bottom">
<p align="center">120</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">476</p>
</td>
<td width="187" valign="bottom">
<p align="center">176</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">526</p>
</td>
<td width="187" valign="bottom">
<p align="center">226</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">588</p>
</td>
<td width="187" valign="bottom">
<p align="center">288</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">625</p>
</td>
<td width="187" valign="bottom">
<p align="center">300</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">650</p>
</td>
<td width="187" valign="bottom">
<p align="center">300</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">675</p>
</td>
<td width="187" valign="bottom">
<p align="center">300</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">700</p>
</td>
<td width="187" valign="bottom">
<p align="center">300</p>
</td>
<td width="199" valign="bottom">
<p align="center">300</p>
</td>
</tr>
</tbody>
</table>
<p align="center">Table I: Matlab data for the 300Hz run</p>
<p>We then searched the data for signs of a mathematical relationship between the original signal, the sampling rate, and the aliased signal, which will be discussed further in the analysis section.</p>
<p>While data was taken at a variety of frequencies and sampling rates, we will focus on three runs – 150Hz, 300Hz, and 472Hz – in this report. The data taken in Matlab for each of these runs is given below:</p>
<p align="center">Figure 6: Matlab data for 150 Hz run</p>
<p>For the 300 Hz run we followed a similar process, starting at 50 samples per second and going up to 420 samples per second. In this trial, the sample size was increased in more random increments to ensure that the results we were seeing weren’t the results of mathematical anomalies. The data from these runs is plotted in the figure below:</p>
<p align="center">Figure 7: Matlab data for the 300 Hz run</p>
<p>We chose to take data at 472 Hz for the same reasons we chose random numbers for the sampling rates in the 300Hz run. After taking data at fairly uninteresting frequencies (100, 150, 200, and 300Hz) we wanted to confirm that our results were consistent at all frequencies. The data for the 472 Hz (and most extensive) run is plotted in the figure below:</p>
<p align="center">Figure 8: Matlab data for the 472 Hz run</p>
<p><strong> </strong></p>
<p><strong>III. EXPERIMENT</strong></p>
<p>A. The Apparatus</p>
<p>After getting an idea of what was happening to our FFTs from the Matlab simulation, we ran a real world experiment to verify that the results were consistent. We used a Hewlett Packard 3310A function generator to create our 150, 300 and 472Hz signals and ran them to a speaker which sent the acoustic signals to a microphone connected to a Vernier LabPro module. The LabPro module then sent the digitized data to a laptop via USB cable and the data was processed by LoggerPro software. A diagram of the experimental setup is shown in Figure 9 below:</p>
<p align="center">
<p>Figure 9: The Experimental Setup</p>
<p>B. Data Collection</p>
<p>LoggerPro FFT results were given in a graph like the one shown below:</p>
<p align="center">Figure 10: A 300Hz signal sampled at 357Hz in LoggerPro</p>
<p>The data was then collected, in much the same way the Matlab data was collected, and put into an Excel spreadsheet for comparison:</p>
<table border="0" cellspacing="0" cellpadding="0" width="488">
<tbody>
<tr>
<td width="143" valign="bottom">
<p align="center">Sample Rate (Hz)</p>
</td>
<td width="212" valign="bottom">
<p align="center">LoggerPro FFT   Results (Hz)</p>
</td>
<td width="133" valign="bottom">Actual Frequency</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">149</p>
</td>
<td width="212" valign="bottom">
<p align="center">2</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">158</p>
</td>
<td width="212" valign="bottom">
<p align="center">17</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">164</p>
</td>
<td width="212" valign="bottom">
<p align="center">28</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">169</p>
</td>
<td width="212" valign="bottom">
<p align="center">39</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">172</p>
</td>
<td width="212" valign="bottom">
<p align="center">45</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">175</p>
</td>
<td width="212" valign="bottom">
<p align="center">50</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">179</p>
</td>
<td width="212" valign="bottom">
<p align="center">57</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">179</p>
</td>
<td width="212" valign="bottom">
<p align="center">57</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">185</p>
</td>
<td width="212" valign="bottom">
<p align="center">70</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">189</p>
</td>
<td width="212" valign="bottom">
<p align="center">77</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">196</p>
</td>
<td width="212" valign="bottom">
<p align="center">91</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">200</p>
</td>
<td width="212" valign="bottom">
<p align="center">99</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">217</p>
</td>
<td width="212" valign="bottom">
<p align="center">84</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">222</p>
</td>
<td width="212" valign="bottom">
<p align="center">79</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">238</p>
</td>
<td width="212" valign="bottom">
<p align="center">63</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">256</p>
</td>
<td width="212" valign="bottom">
<p align="center">45</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">263</p>
</td>
<td width="212" valign="bottom">
<p align="center">38</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">270</p>
</td>
<td width="212" valign="bottom">
<p align="center">31</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">278</p>
</td>
<td width="212" valign="bottom">
<p align="center">23</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">303</p>
</td>
<td width="212" valign="bottom">
<p align="center">2</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">323</p>
</td>
<td width="212" valign="bottom">
<p align="center">22</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">333</p>
</td>
<td width="212" valign="bottom">
<p align="center">32</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">345</p>
</td>
<td width="212" valign="bottom">
<p align="center">44</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">357</p>
</td>
<td width="212" valign="bottom">
<p align="center">56</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">385</p>
</td>
<td width="212" valign="bottom">
<p align="center">84</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">400</p>
</td>
<td width="212" valign="bottom">
<p align="center">99</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">417</p>
</td>
<td width="212" valign="bottom">
<p align="center">116</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">417</p>
</td>
<td width="212" valign="bottom">
<p align="center">116</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">476</p>
</td>
<td width="212" valign="bottom">
<p align="center">175</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">526</p>
</td>
<td width="212" valign="bottom">
<p align="center">225</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">588</p>
</td>
<td width="212" valign="bottom">
<p align="center">287</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">625</p>
</td>
<td width="212" valign="bottom">
<p align="center">302</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">667</p>
</td>
<td width="212" valign="bottom">
<p align="center">302</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">675</p>
</td>
<td width="212" valign="bottom">
<p align="center">302</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">700</p>
</td>
<td width="212" valign="bottom">
<p align="center">302</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">196</p>
</td>
<td width="212" valign="bottom">
<p align="center">91</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">200</p>
</td>
<td width="212" valign="bottom">
<p align="center">99</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">217</p>
</td>
<td width="212" valign="bottom">
<p align="center">84</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">222</p>
</td>
<td width="212" valign="bottom">
<p align="center">79</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">238</p>
</td>
<td width="212" valign="bottom">
<p align="center">63</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">256</p>
</td>
<td width="212" valign="bottom">
<p align="center">45</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">263</p>
</td>
<td width="212" valign="bottom">
<p align="center">38</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">270</p>
</td>
<td width="212" valign="bottom">
<p align="center">31</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">278</p>
</td>
<td width="212" valign="bottom">
<p align="center">23</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">303</p>
</td>
<td width="212" valign="bottom">
<p align="center">2</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">323</p>
</td>
<td width="212" valign="bottom">
<p align="center">22</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">333</p>
</td>
<td width="212" valign="bottom">
<p align="center">32</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">345</p>
</td>
<td width="212" valign="bottom">
<p align="center">44</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">357</p>
</td>
<td width="212" valign="bottom">
<p align="center">56</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">385</p>
</td>
<td width="212" valign="bottom">
<p align="center">84</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">400</p>
</td>
<td width="212" valign="bottom">
<p align="center">99</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">417</p>
</td>
<td width="212" valign="bottom">
<p align="center">116</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">417</p>
</td>
<td width="212" valign="bottom">
<p align="center">116</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">476</p>
</td>
<td width="212" valign="bottom">
<p align="center">175</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">526</p>
</td>
<td width="212" valign="bottom">
<p align="center">225</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">588</p>
</td>
<td width="212" valign="bottom">
<p align="center">287</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">625</p>
</td>
<td width="212" valign="bottom">
<p align="center">302</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">667</p>
</td>
<td width="212" valign="bottom">
<p align="center">302</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">675</p>
</td>
<td width="212" valign="bottom">
<p align="center">302</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">700</p>
</td>
<td width="212" valign="bottom">
<p align="center">302</p>
</td>
<td width="133" valign="bottom">
<p align="center">300</p>
</td>
</tr>
</tbody>
</table>
<p align="center">
<p align="center">Table 2: Excel spreadsheet for the 300Hz LoggerPro run</p>
<p>The data showed that our experimental LoggerPro results verified our simulated Matlab results.</p>
<p>The experimental data taken for each of the three runs was plotted and is given in figures 11 through 13 below:</p>
<p align="center">
<p align="center">Figure 11: LoggerPro data for the 150Hz run</p>
<p align="center">
<p align="center">Figure 12: LoggerPro data for the 300Hz run</p>
<p align="center">Figure 13: LoggerPro data for a 472Hz run</p>
<p><strong>IV. ANALYSIS</strong></p>
<p>As you can see from Table I and Figures 6 through 8, the FFT result goes through alternating periods of increasing and decreasing frequency. Looking closer at our range of interest (sampling rate between F<sub>N</sub> &lt; R &lt; F<sub>S</sub>), we see that certain patterns run through each set of data.</p>
<p>In Table 1, when the sampling rate is anywhere from ½ to 2/3 the actual analog signal frequency (150 to 200 Hz), we found that the Matlab FFT results increased at a rate given by the equation:</p>
<p>2 F<sub>N</sub> – F<sub>0</sub> = F<sub>S</sub></p>
<p align="center">Equation 3: Sampling rate is ½ to 2/3 the actual frequency</p>
<p>Where F<sub>N</sub> is the Nyquist frequency for the particular sampling rate being used, F<sub>0</sub> is the frequency of the aliased signal (Matlab FFT result), and F<sub>S</sub> is the frequency of the actual analog signal.</p>
<p>When the sampling rate is anywhere between 2/3 to 1 times the actual signal frequency (200 to 300 Hz), we found that the Matlab FFT results decreased at a rate given by the equation:</p>
<p>2 F<sub>N</sub> + F<sub>0</sub> = F<sub>S</sub></p>
<p align="center">Equation 4: Sampling rate is 2/3 to 1 times the actual frequency</p>
<p>When the sampling rate ranges from equal to the analog frequency to twice the analog frequency (the point at which undersampling ceases and aliasing is no longer a problem – 300 to 600 Hz), we found that the Matlab FFT results increased at a rate given by the equation:</p>
<p>4 F<sub>N</sub> – F<sub>0</sub> = F<sub>S</sub></p>
<p align="center">Equation 5: Sampling rate is 1 to 2 times the actual frequency</p>
<p>At any sampling rate exceeding this the Matlab FFT consistently returned accurate results (as expected).</p>
<p><strong>V. CONCLUSION </strong></p>
<p>Our findings showed that aliased data could be salvaged to a certain extent. Equations 3 through 5 require the sampling rate to be at least half of the highest frequency component of the signal of interest and even then, there is some uncertainty in the results they give. Part of the problem with aliased data is not knowing which signals are valid and which are false. Without being able to retake the data, the researcher must create several scenarios in which each signal is considered valid, each signal is considered aliased, and all the combinations in between.</p>
<p>However, these results are better than no results at all and in cases where the signal has a relatively small number of component frequencies, our method can breath new life into valuable data.</p>
<p align="center"><strong>APPENDIX</strong></p>
<ol>
<li><strong>sampling.m      Matlab Program Code</strong></li>
</ol>
<p>% sampling.m (mjm 8/28/07)</p>
<p>%</p>
<p>clear</p>
<p>clf</p>
<p>A=1.0; B=0;</p>
<p>% 10 000 points in 1 second, data every 0.0001 seconds</p>
<p>totsteps=100000;</p>
<p>timestep=1/totsteps;</p>
<p>t=0:timestep:1;</p>
<p>f1=472; f2=f1;</p>
<p>y=A*sin(2*pi*f1*t)+B*sin(2*pi*f2*t);     % f and 2f signal</p>
<p>subplot(2,1,1)</p>
<p>plot(t,y)</p>
<p>title(['frequencies: ',num2str(f1),', ',num2str(f2)])</p>
<p>ylabel(&#8217;signal&#8217;)</p>
<p>xlabel(&#8217;time (s)&#8217;)</p>
<p>hold on</p>
<p>% now choose just some of signal</p>
<p>%</p>
<p>fsamp=60;</p>
<p>step=totsteps/fsamp;</p>
<p>ySamp=y(1:step:length(y));</p>
<p>% now plot sampled data</p>
<p>plot(t(1:step:length(y)),ySamp,&#8217;ko&#8217;)</p>
<p>%</p>
<p>FFTySamp = fft(ySamp);</p>
<p>freq=fsamp*linspace(0,1,length(ySamp));</p>
<p>PSDySamp = FFTySamp.* conj(FFTySamp) / length(ySamp);</p>
<p>subplot(2,1,2)</p>
<p>%plot(freq(1:length(freq)/2), PSDySamp(1:length(freq)/2))</p>
<p>plot(freq,PSDySamp)</p>
<p>title(['power spectral density, f_{samp}= ',num2str(fsamp)])</p>
<p>ylabel(&#8217;PSD&#8217;)</p>
<p>xlabel(&#8217;freq&#8217;)</p>
<p>%</p>
<ol>
<li><strong>150Hz Matlab      Excel Data</strong></li>
</ol>
<table border="0" cellspacing="0" cellpadding="0" width="343">
<tbody>
<tr>
<td width="156" valign="bottom">
<p align="center">Sampling Rate   (Hz)</p>
</td>
<td width="187" valign="bottom">
<p align="center">Matlab FFT   Results (Hz)</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">27</p>
</td>
<td width="187" valign="bottom">
<p align="center">13</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">28</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">29</p>
</td>
<td width="187" valign="bottom">
<p align="center">5</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">30</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">31</p>
</td>
<td width="187" valign="bottom">
<p align="center">5</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">32</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">33</p>
</td>
<td width="187" valign="bottom">
<p align="center">16</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">34</p>
</td>
<td width="187" valign="bottom">
<p align="center">14</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">35</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">36</p>
</td>
<td width="187" valign="bottom">
<p align="center">6</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">37</p>
</td>
<td width="187" valign="bottom">
<p align="center">2</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">38</p>
</td>
<td width="187" valign="bottom">
<p align="center">2</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">39</p>
</td>
<td width="187" valign="bottom">
<p align="center">6</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">40</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">45</p>
</td>
<td width="187" valign="bottom">
<p align="center">15</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">49</p>
</td>
<td width="187" valign="bottom">
<p align="center">3</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">51</p>
</td>
<td width="187" valign="bottom">
<p align="center">3</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">52</p>
</td>
<td width="187" valign="bottom">
<p align="center">6</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">55</p>
</td>
<td width="187" valign="bottom">
<p align="center">15</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">60</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">65</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">70</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">72</p>
</td>
<td width="187" valign="bottom">
<p align="center">6</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">74</p>
</td>
<td width="187" valign="bottom">
<p align="center">3</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">76</p>
</td>
<td width="187" valign="bottom">
<p align="center">2</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">77</p>
</td>
<td width="187" valign="bottom">
<p align="center">4</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">80</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">85</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">90</p>
</td>
<td width="187" valign="bottom">
<p align="center">30</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">95</p>
</td>
<td width="187" valign="bottom">
<p align="center">40</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">99</p>
</td>
<td width="187" valign="bottom">
<p align="center">49</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">101</p>
</td>
<td width="187" valign="bottom">
<p align="center">50</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">105</p>
</td>
<td width="187" valign="bottom">
<p align="center">45</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">110</p>
</td>
<td width="187" valign="bottom">
<p align="center">40</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">115</p>
</td>
<td width="187" valign="bottom">
<p align="center">35</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">120</p>
</td>
<td width="187" valign="bottom">
<p align="center">30</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">125</p>
</td>
<td width="187" valign="bottom">
<p align="center">25</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">130</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">135</p>
</td>
<td width="187" valign="bottom">
<p align="center">15</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">140</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">145</p>
</td>
<td width="187" valign="bottom">
<p align="center">5</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">151</p>
</td>
<td width="187" valign="bottom">
<p align="center">0</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">155</p>
</td>
<td width="187" valign="bottom">
<p align="center">5</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">160</p>
</td>
<td width="187" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">165</p>
</td>
<td width="187" valign="bottom">
<p align="center">15</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">170</p>
</td>
<td width="187" valign="bottom">
<p align="center">20</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">175</p>
</td>
<td width="187" valign="bottom">
<p align="center">25</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">180</p>
</td>
<td width="187" valign="bottom">
<p align="center">30</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">190</p>
</td>
<td width="187" valign="bottom">
<p align="center">40</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">200</p>
</td>
<td width="187" valign="bottom">
<p align="center">50</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">210</p>
</td>
<td width="187" valign="bottom">
<p align="center">60</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">220</p>
</td>
<td width="187" valign="bottom">
<p align="center">70</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">230</p>
</td>
<td width="187" valign="bottom">
<p align="center">80</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">240</p>
</td>
<td width="187" valign="bottom">
<p align="center">90</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">251</p>
</td>
<td width="187" valign="bottom">
<p align="center">101</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">260</p>
</td>
<td width="187" valign="bottom">
<p align="center">110</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">270</p>
</td>
<td width="187" valign="bottom">
<p align="center">120</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">280</p>
</td>
<td width="187" valign="bottom">
<p align="center">130</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">290</p>
</td>
<td width="187" valign="bottom">
<p align="center">141</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">295</p>
</td>
<td width="187" valign="bottom">
<p align="center">146</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">299</p>
</td>
<td width="187" valign="bottom">
<p align="center">150</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">305</p>
</td>
<td width="187" valign="bottom">
<p align="center">150</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">310</p>
</td>
<td width="187" valign="bottom">
<p align="center">150</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">320</p>
</td>
<td width="187" valign="bottom">
<p align="center">150</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">330</p>
</td>
<td width="187" valign="bottom">
<p align="center">150</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">340</p>
</td>
<td width="187" valign="bottom">
<p align="center">150</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">350</p>
</td>
<td width="187" valign="bottom">
<p align="center">150</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">360</p>
</td>
<td width="187" valign="bottom">
<p align="center">150</p>
</td>
</tr>
</tbody>
</table>
<p align="center">
<ol>
<li><strong>472Hz Matlab      Excel Data</strong></li>
</ol>
<table border="0" cellspacing="0" cellpadding="0" width="329">
<tbody>
<tr>
<td width="143" valign="bottom">Sample   Rate (Hz)</td>
<td width="187" valign="bottom">Matlab   FFT Results (Hz)</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">230</p>
</td>
<td width="187" valign="bottom">
<p align="center">12</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">250</p>
</td>
<td width="187" valign="bottom">
<p align="center">28</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">270</p>
</td>
<td width="187" valign="bottom">
<p align="center">68</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">290</p>
</td>
<td width="187" valign="bottom">
<p align="center">108</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">310</p>
</td>
<td width="187" valign="bottom">
<p align="center">148</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">330</p>
</td>
<td width="187" valign="bottom">
<p align="center">142</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">350</p>
</td>
<td width="187" valign="bottom">
<p align="center">122</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">370</p>
</td>
<td width="187" valign="bottom">
<p align="center">102</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">390</p>
</td>
<td width="187" valign="bottom">
<p align="center">82</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">410</p>
</td>
<td width="187" valign="bottom">
<p align="center">62</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">430</p>
</td>
<td width="187" valign="bottom">
<p align="center">42</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">450</p>
</td>
<td width="187" valign="bottom">
<p align="center">22</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">470</p>
</td>
<td width="187" valign="bottom">
<p align="center">2</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">490</p>
</td>
<td width="187" valign="bottom">
<p align="center">18</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">510</p>
</td>
<td width="187" valign="bottom">
<p align="center">38</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">530</p>
</td>
<td width="187" valign="bottom">
<p align="center">58</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">550</p>
</td>
<td width="187" valign="bottom">
<p align="center">78</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">570</p>
</td>
<td width="187" valign="bottom">
<p align="center">98</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">590</p>
</td>
<td width="187" valign="bottom">
<p align="center">118</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">610</p>
</td>
<td width="187" valign="bottom">
<p align="center">138</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">630</p>
</td>
<td width="187" valign="bottom">
<p align="center">158</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">650</p>
</td>
<td width="187" valign="bottom">
<p align="center">178</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">670</p>
</td>
<td width="187" valign="bottom">
<p align="center">198</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">690</p>
</td>
<td width="187" valign="bottom">
<p align="center">218</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">710</p>
</td>
<td width="187" valign="bottom">
<p align="center">238</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">750</p>
</td>
<td width="187" valign="bottom">
<p align="center">278</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">775</p>
</td>
<td width="187" valign="bottom">
<p align="center">303</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">800</p>
</td>
<td width="187" valign="bottom">
<p align="center">328</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">825</p>
</td>
<td width="187" valign="bottom">
<p align="center">353</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">850</p>
</td>
<td width="187" valign="bottom">
<p align="center">378</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">875</p>
</td>
<td width="187" valign="bottom">
<p align="center">404</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">900</p>
</td>
<td width="187" valign="bottom">
<p align="center">428</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">925</p>
</td>
<td width="187" valign="bottom">
<p align="center">453</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">950</p>
</td>
<td width="187" valign="bottom">
<p align="center">473</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">975</p>
</td>
<td width="187" valign="bottom">
<p align="center">472</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">1000</p>
</td>
<td width="187" valign="bottom">
<p align="center">472</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">1025</p>
</td>
<td width="187" valign="bottom">
<p align="center">472</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">1050</p>
</td>
<td width="187" valign="bottom">
<p align="center">472</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">1075</p>
</td>
<td width="187" valign="bottom">
<p align="center">472</p>
</td>
</tr>
<tr>
<td width="143" valign="bottom">
<p align="center">1100</p>
</td>
<td width="187" valign="bottom">
<p align="center">472</p>
</td>
</tr>
</tbody>
</table>
<p><strong> </strong></p>
<p><strong> </strong></p>
<ol>
<li><strong>150Hz      LoggerPro Excel Data</strong></li>
</ol>
<table border="0" cellspacing="0" cellpadding="0" width="368">
<tbody>
<tr>
<td width="156" valign="bottom">Sampling   Rate (Hz)</td>
<td width="212" valign="bottom">LoggerPro   FFT Results (Hz)</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">74</p>
</td>
<td width="212" valign="bottom">
<p align="center">3</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">76</p>
</td>
<td width="212" valign="bottom">
<p align="center">0</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">77</p>
</td>
<td width="212" valign="bottom">
<p align="center">3</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">80</p>
</td>
<td width="212" valign="bottom">
<p align="center">9</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">85</p>
</td>
<td width="212" valign="bottom">
<p align="center">19</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">90</p>
</td>
<td width="212" valign="bottom">
<p align="center">29</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">95</p>
</td>
<td width="212" valign="bottom">
<p align="center">40</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">99</p>
</td>
<td width="212" valign="bottom">
<p align="center">47</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">101</p>
</td>
<td width="212" valign="bottom">
<p align="center">50</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">105</p>
</td>
<td width="212" valign="bottom">
<p align="center">46</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">110</p>
</td>
<td width="212" valign="bottom">
<p align="center">42</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">115</p>
</td>
<td width="212" valign="bottom">
<p align="center">37</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">120</p>
</td>
<td width="212" valign="bottom">
<p align="center">31</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">125</p>
</td>
<td width="212" valign="bottom">
<p align="center">26</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">130</p>
</td>
<td width="212" valign="bottom">
<p align="center">21</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">135</p>
</td>
<td width="212" valign="bottom">
<p align="center">16</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">140</p>
</td>
<td width="212" valign="bottom">
<p align="center">10</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">158</p>
</td>
<td width="212" valign="bottom">
<p align="center">9</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">164</p>
</td>
<td width="212" valign="bottom">
<p align="center">14</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">169</p>
</td>
<td width="212" valign="bottom">
<p align="center">19</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">172</p>
</td>
<td width="212" valign="bottom">
<p align="center">22</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">175</p>
</td>
<td width="212" valign="bottom">
<p align="center">26</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">179</p>
</td>
<td width="212" valign="bottom">
<p align="center">28</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">179</p>
</td>
<td width="212" valign="bottom">
<p align="center">28</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">185</p>
</td>
<td width="212" valign="bottom">
<p align="center">35</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">189</p>
</td>
<td width="212" valign="bottom">
<p align="center">39</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">196</p>
</td>
<td width="212" valign="bottom">
<p align="center">46</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">200</p>
</td>
<td width="212" valign="bottom">
<p align="center">50</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">217</p>
</td>
<td width="212" valign="bottom">
<p align="center">67</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">222</p>
</td>
<td width="212" valign="bottom">
<p align="center">72</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">238</p>
</td>
<td width="212" valign="bottom">
<p align="center">87</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">256</p>
</td>
<td width="212" valign="bottom">
<p align="center">106</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">263</p>
</td>
<td width="212" valign="bottom">
<p align="center">113</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">278</p>
</td>
<td width="212" valign="bottom">
<p align="center">127</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">303</p>
</td>
<td width="212" valign="bottom">
<p align="center">150</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">323</p>
</td>
<td width="212" valign="bottom">
<p align="center">151</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">333</p>
</td>
<td width="212" valign="bottom">
<p align="center">151</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">345</p>
</td>
<td width="212" valign="bottom">
<p align="center">151</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">357</p>
</td>
<td width="212" valign="bottom">
<p align="center">151</p>
</td>
</tr>
</tbody>
</table>
<p><strong> </strong></p>
<p><strong> </strong></p>
<ol>
<li><strong>472Hz      LoggerPro Excel Data</strong></li>
</ol>
<table border="0" cellspacing="0" cellpadding="0" width="368">
<tbody>
<tr>
<td width="156" valign="bottom">
<p align="center">Sampling Rate   (Hz)</p>
</td>
<td width="212" valign="bottom">
<p align="center">LoggerPro FFT   Results (Hz)</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">232</p>
</td>
<td width="212" valign="bottom">
<p align="center">5</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">250</p>
</td>
<td width="212" valign="bottom">
<p align="center">30</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">270</p>
</td>
<td width="212" valign="bottom">
<p align="center">70</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">294</p>
</td>
<td width="212" valign="bottom">
<p align="center">118</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">312</p>
</td>
<td width="212" valign="bottom">
<p align="center">155</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">333</p>
</td>
<td width="212" valign="bottom">
<p align="center">137</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">344</p>
</td>
<td width="212" valign="bottom">
<p align="center">125</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">370</p>
</td>
<td width="212" valign="bottom">
<p align="center">100</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">384</p>
</td>
<td width="212" valign="bottom">
<p align="center">86</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">416</p>
</td>
<td width="212" valign="bottom">
<p align="center">54</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">434</p>
</td>
<td width="212" valign="bottom">
<p align="center">36</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">454</p>
</td>
<td width="212" valign="bottom">
<p align="center">16</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">476</p>
</td>
<td width="212" valign="bottom">
<p align="center">6</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">526</p>
</td>
<td width="212" valign="bottom">
<p align="center">30</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">526</p>
</td>
<td width="212" valign="bottom">
<p align="center">30</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">526</p>
</td>
<td width="212" valign="bottom">
<p align="center">30</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">555</p>
</td>
<td width="212" valign="bottom">
<p align="center">70</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">555</p>
</td>
<td width="212" valign="bottom">
<p align="center">70</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">588</p>
</td>
<td width="212" valign="bottom">
<p align="center">118</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">625</p>
</td>
<td width="212" valign="bottom">
<p align="center">155</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">625</p>
</td>
<td width="212" valign="bottom">
<p align="center">155</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">667</p>
</td>
<td width="212" valign="bottom">
<p align="center">196</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">667</p>
</td>
<td width="212" valign="bottom">
<p align="center">196</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">714</p>
</td>
<td width="212" valign="bottom">
<p align="center">244</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">714</p>
</td>
<td width="212" valign="bottom">
<p align="center">244</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">769</p>
</td>
<td width="212" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">769</p>
</td>
<td width="212" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">769</p>
</td>
<td width="212" valign="bottom">
<p align="center">300</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">833</p>
</td>
<td width="212" valign="bottom">
<p align="center">364</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">833</p>
</td>
<td width="212" valign="bottom">
<p align="center">364</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">909</p>
</td>
<td width="212" valign="bottom">
<p align="center">440</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">909</p>
</td>
<td width="212" valign="bottom">
<p align="center">440</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">1000</p>
</td>
<td width="212" valign="bottom">
<p align="center">470</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">1000</p>
</td>
<td width="212" valign="bottom">
<p align="center">470</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">1000</p>
</td>
<td width="212" valign="bottom">
<p align="center">470</p>
</td>
</tr>
<tr>
<td width="156" valign="bottom">
<p align="center">1000</p>
</td>
<td width="212" valign="bottom">
<p align="center">470</p>
</td>
</tr>
</tbody>
</table>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p align="center"><strong>BIBLIOGRAPHY</strong></p>
<p><sup>1</sup>E. O. Brigham, <em>The Fast Fourier Transform and it’s Applications</em> (Prentice-Hall, Englewood Cliffs, 1988) p. 84</p>
<p><sup>2</sup>R. W. Ramirez, <em>The FFT: Fundamentals and Concepts</em> (Prentice-Hall, Englewood Cliffs, 1985) pp. 115-123</p>
<p><sup>3</sup> E. O. Brigham, <em>The Fast Fourier Transform and it’s Applications</em> (Prentice-Hall, Englewood Cliffs, 1988) p. 9</p>
<p><sup>4</sup> R. W. Ramirez, <em>The FFT: Fundamentals and Concepts</em> (Prentice-Hall, Englewood Cliffs, 1985) p. 67</p>
<p><sup>5</sup> E. O. Brigham, <em>The Fast Fourier Transform and it’s Applications</em> (Prentice-Hall, Englewood Cliffs, 1988) p. 365</p>
]]></content:encoded>
			<wfw:commentRss>http://marinemammalconservancy.org/research/methods-for-salvaging-undersampled-acoustic-data-by-shaun-t-perisho/feed</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Training of Castaway</title>
		<link>http://marinemammalconservancy.org/research/training-of-castaway</link>
		<comments>http://marinemammalconservancy.org/research/training-of-castaway#comments</comments>
		<pubDate>Wed, 28 Oct 2009 01:09:21 +0000</pubDate>
		<dc:creator>Bob</dc:creator>
				<category><![CDATA[MMC Research]]></category>
		<category><![CDATA[Research]]></category>
		<category><![CDATA[castaway]]></category>

		<guid isPermaLink="false">http://marinemammalconservancy.org/?p=1445</guid>
		<description><![CDATA[<strong>Contacting “Castaway”: Training a Wild, Deaf, Offshore Atlantic bottlenose Dolphin (Tursiops truncatus)</strong>
Sarah C. Sayre1, Nancy Cooper1 , Stacey J. Anderson2, Jill Richardso&#8230;]]></description>
			<content:encoded><![CDATA[<p align="center"><strong>Contacting “Castaway”: Training a Wild, Deaf, Offshore Atlantic bottlenose Dolphin (<em>Tursiops truncatus</em>)</strong></p>
<p align="center">Sarah C. Sayre<sup>1</sup>, Nancy Cooper<sup>1 </sup>, Stacey J. Anderson<sup>2</sup>, Jill Richardson<sup>1,2</sup></p>
<p align="center">
<ol>
<li><em>Dolphins Plus      Inc., 31 Corinne Place, Key Largo, FL 33037 (education@dolphinsplus.com)</em></li>
<li><em>Marine Mammal      Conservancy, P.O. Box 1625, Key Largo, FL 33037      (rgl@marinemammalconservancy.org)</em></li>
</ol>
<p align="center"><strong> </strong></p>
<p align="center"><strong>History</strong></p>
<p>Castaway, a deaf, visually impaired, neurologically challenged, offshore Atlantic Bottlenose dolphin (<em>Tursiops truncatus</em>) was found stranded on Castaway Cove beach, Vero Beach (Florida, USA) on 11, November 2006.  Harbor Branch Oceanographic Institute (HBOI) responded <em>in situ</em>, and she was subsequently transported to Mote Marine Laboratory (Mote) in Sarasota, Florida.  After 79 days of rehabilitation, four unsuccessful release attempts on 30, January 2007 culminated in her transport to Marine Mammal Conservancy (MMC) in Key Largo, Florida.  Castaway remained at MMC for approximately six months, where she was housed in various Florida Bay, natural lagoon settings (depth and size ranges: 3 – 6 m depth; 165 m<sup>2</sup> – 3300 m<sup>2</sup> enclosed area) and isolated from conspecifics.</p>
<p>Two days after Castaway arrived at MMC, a remarkable lack of response to auditory stimuli (e.g. “pingers” and tapping a partially submerged stainless steel bucket) was noted.  Suspicion of her deafness was confirmed via two passive auditory tests conducted by Dr. David Mann (University of South Florida) on 18, February 2007.  In addition to her hearing deficits, Castaway’s left eye displayed mild to moderate impairment, and possible neurological deficiencies were noted.  Castaway was remarkably maladroit, with weak gross motor coordination, lacked interest in or focus on environmental stimuli, and appeared unable to recognize patterns.  Though her capacity for response improved slowly over the course of six months at MMC, her anomalous mannerisms and limitations presented many training and enrichment challenges.</p>
<p>Castaway was transported to Dolphins Plus on 25 July 2007, where she currently resides with two adult female conspecifics in a natural lagoon setting (approximate depth and area: 4.5 m and 388 m<sup>2</sup>).</p>
<p align="center"><strong>Training</strong></p>
<p>While at MMC, Castaway’s inability to hear, compounded by her solitary confinement, inertness, and deficient attention span, had a large impact on her training in both formal and informal sessions.  At the commencement of her training regimen, primary reinforcement was established (i.e. herring) as the predominant training tool.  In general, her training sessions at MMC were short, and the criteria for success were low.  After she moved to Dolphins Plus, her focus improved dramatically, and thus the training criteria were much more stringent.</p>
<p align="center"><strong>Targeting</strong></p>
<p>In order to acquire Castaway to station for feeds at MMC, fist targeting was implemented immediately.  Presentations of a human fist were rigorous to ensure detection, and general orienting was immediately rewarding with an Atlantic herring (<em>Clupea harengus)</em> underwater.  Within three to five sessions (minimum of 15 trials session<sup>-1</sup>), Castaway was performing the response with approximately 100% success.  However, Castaway was still under rehabilitative care, so the criteria for targeting were broad.  Due to the large size of Castaway’s lagoon, a physical approach by staff to acquire and guide her to station was necessary.  Though Castaway’s feeding station and times were consistent over six months, she never anticipated a feed while at MMC.</p>
<p>Once fist targeting was established, the transition to a target pole was virtually effortless.  The presentation of the target pole was paired with a fist and contact with both elicited primary reinforcement.  After the first pairing, no other approximations were necessary, because Castaway was targeting on the pole upon presentation with 100% success.</p>
<p align="center"><strong>Recall</strong></p>
<p>The laborious exercise of entering Castaway’s enclosure at MMC to retrieve her to station for feeding resulted in the implementation of a strobe light for recall purposes.  Castaway’s inability to hear precluded the use of traditional auditory recall methods, so the strobe light was substituted as a visual cue.  The strobe was initially presented within visual range and contact with the light source was paired with primary reinforcement.  Shaping involved the presentation of the light at various distances (approximate range = 1.5 – 9 m) and orientation towards the strobe eventually developed into a directed approach.  Though the strobe proved to be an effective recall, it was limited in range (i.e. required proximate presentation), and its effectiveness was heavily dependent upon the physical conditions of her natural lagoon (e.g. turbidity).  Thus, the necessity of entering the water to station and recall Castaway remained unavoidable.</p>
<p>When Castaway was transferred to Dolphins Plus, an attempt was made to solve the problems associated with a “long-distance” recall by employing the use of a toy water cannon.  This was implemented, because Castaway was noted to respond to proximate water displacement or disruption while at MMC.  In order for the water cannon to be effective, the splash needed to fall within her visual range, or contact her directly.  Castaway’s orientation towards the splash was consistently rewarded with primary reinforcement, and this application remains in place as the most effective recall method at Dolphins Plus to date.</p>
<p align="center"><strong>Pattern Recognition</strong></p>
<p>While at MMC, Castaway’s ability to recognize patterns, and thereby exhibit an anticipatory response to a repeated sequence, was tested via rudimentary A to B feeding trials.  Two feeders were separated by approximately 0.5 m at her feeding station.  Each feeder paired the presentation of the strobe light in close range of her eye with primary reinforcement, alternating sides of the bilateral axis.  The hypothesis was that Castaway would eventually anticipate the presentation of the strobe and reward by swinging her head side to side.  This protocol was replicated over the course of two weeks, up to seven times day<sup>-1</sup>, and no anticipation was noted (multiple observers).</p>
<p>Castaway’s capacity to recognize patterns was re-tested at Dolphins Plus in October 2007.  Trials (n = 9) were designed to replicate the MMC experiment, using two trainers separated by 1.2m at Castaway’s feeding station.  In place of a strobe, each trainer alternated slapping the surface of the water, followed by the presentation of primary reinforcement.  Each trial involved 40 presentations, and the response time was limited to five seconds.  After the last presentation, both trainers remained motionless, and Castaway’s response was recorded.  Castaway exhibited no response in three trials and an opposite response in one.  However, she successfully anticipated the pattern in five of the nine trials.  Thus, this experiment was a verification of her improved cognitive condition.</p>
<p align="center"><strong>Vertical Positioning</strong></p>
<p>Once stationing was achieved, Castaway was trained to accept food in a vertical position, with her head and eyes above the water.  This proved to be a very arduous task.  Castaway initially exhibited a reluctance or inability (reasoning is unclear) to lift her head above the water.  While at MMC, and during her first month at Dolphins Plus, Castaway almost never acknowledged above-water activity, and she was never observed craning, spy-hopping, or bowing when this training commenced.  Due to the fact that an appropriate bridge had not yet been established, primary reinforcement was used to convey success.  The target pole was utilized as a tool, and slight approximations were “jack-potted” to impart this seemingly difficult concept.  Her progress during this initial stage of training was painstakingly slow, and consistent, focused training for two and a half weeks was necessary to achieve rostral contact with the pole presented just above the surface of the water.  Once contact with the target pole, while in a vertical position, was established as a successful response, regular increases in the distance of the target pole from the surface of the water resulted in 100% success of the targeted behavior in four days.</p>
<p align="center"><strong>The Bridge</strong></p>
<p>Once at Dolphins Plus, the development of a non-auditory bridge was crucial to Castaway’s development.  The coastal Atlantic bottlenose dolphin population at Dolphins Plus is conditioned to respond to athletic whistles as an auditory bridge.  These whistles are very effective in terms of dolphin response and are also utilized to convey the termination of a behavior to guest swimmers.  Consideration of an appropriate non-auditory bridge for Castaway included the use of pneumatics, a board or paddle, and a pointing gesture.  The point bridge has been utilized with great success in other marine mammals (e.g. polar bears, Belting et. al 1998; sea lions, MaGee 2007, personal communication) but proved to be a very difficult application with Castaway.  The point bridge involved the pairing of an exaggerated, direct, finger point towards Castaway’s dominant, right eye with primary reinforcement.  Castaway’s learning curve was extremely slow, and four months of consistent replication was required to obtain an 85% success rate.  Castaway’s biggest impediment to improvement was what appeared to be signs of short-term memory loss.  For example, when she appeared to understand the concept of the point bridge while at station, she could not apply that concept to other behaviors.  Thus, the bridge training had to be re-instated with every new behavior.  Plausible theories for Castaway’s deficient/impaired ability to learn include her inability to hear, neurological impairment, and her classification as an offshore bottlenose dolphin.</p>
<p>There are inherent limitations of a point bridge, predominantly the necessity of proximate application.  Castaway must be within close range of the presentation of the point bridge and must be looking at her trainer in order for it to be effective.  Thus, capturing behaviors at appropriate or apex moments is very difficult.  A vast majority of auditory bridges function at relatively long distances between the trainer and the animal and are also omni-directional.  Thus, the necessity of utilizing visual cues undeniably puts Castaway at a learning disadvantage.</p>
<p align="center"><strong>Secondary Reinforcement</strong></p>
<p>While at MMC, Castaway presented as an overtly tactile animal and was frequently observed rubbing fences, platforms, limestone rocks, and ropes.  Thus, a scrub brush was applied as secondary reinforcement.  Vigorous scrubbing from her trainers was utilized as a reward for remaining at station and completing various tasks.  The limitations of using only primary reinforcement with Castaway involved her desire to minimize the time between performing a response and the delivery of food.  Thus, the use of the scrub brush as a secondary reinforcer was pivotal in Castaway’s training, because she learned to hold requested responses and positions (e.g. husbandry behaviors) for longer periods of time.  This aspect of her training resulted in a dramatic improvement in her ability to learn behaviors, including moving rubs and dorsal and pectoral presentations.</p>
<p>The effectiveness and “value” of the scrub brush as a secondary reinforcer was stimulated by pairing scrubbing with trainer swim interactions.  These interactions eventually became more reinforcing to Castaway than primary reinforcement.  Her trainers entered the water after successful training sessions, wearing mask, fins, and snorkel, and essentially “scrubbed” her.  This interaction became a tool to entice a very sedentary animal to exercise, because she was eventually required to actively swim to receive a brush-down.  To date, this appears to be Castaway’s preferred activity and serves as a great relationship-builder between Castaway and her trainers.</p>
<p><strong> </strong></p>
<p align="center"><strong>Enrichment</strong></p>
<p>While at MMC, environmental enrichment devices (EEDs), such as hula-hoops, balls, and bath toys, initially elicited little to no response from Castaway, with the exception of the rub rope.  The activities that consistently prompted a response from Castaway were trainer swim interactions.  Thus, while at MMC, staff swims with Castaway were encouraged, accounting for three to eight swims day<sup>-1</sup> for one month.  This activity provided a source of enrichment and prepared Castaway for the Dolphins Plus public natural swim program.  During a natural swim, the dolphins are not at control and are not offered any reinforcement beyond that received from human-dolphin swim interactions.  Though Castaway’s response to individuals other than her trainers was slow at both MMC and Dolphins Plus, interactions between staff were encouraged with a fluke-tow.  During the tow, trainers pulled Castaway backwards by her flukes for a few seconds, which elicited an active swimming response upon release.  Eventually, the fluke-tow was phased out, and Castaway actively sought out swimmers, frequently engaging in side-by-side swim interactions.</p>
<p align="center"><strong>Behavioral Inventory</strong></p>
<p>With the application of the point bridge, and the use of the scrub brush as an effective secondary reinforcer, Castaway accomplished the following behaviors with an 85% success rate over the course of three months at Dolphins Plus: open/close mouth, tongue presentation, eye cup, high and low targets, blowing bubbles, toy retrieval (e.g. ball, ring, propeller), bilateral pectoral presentation, short distance A to Bs, dorsal presentation, and moving dorsal rubs.  These behaviors were trained using shaping and capturing.  This learning “explosion” is attributed in part to the possibility of improved neurological function and hearing and increased social stimulation.</p>
<p align="center"><strong>Acknowledgements</strong></p>
<p>We would like to acknowledge the founder and president of the Marine Mammal Conservancy, Robert Lingenfelser, for his dedication to Castaway’s rehabilitation and well-being.  Staff and volunteer veterinarian Robert Stevens was crucial in maintaining Castaway’s health and remains a consistent source of support and guidance.  We would like to extend our deepest gratitude to all of the MMC volunteers and Dolphins Plus staff for their hard work and participation with care and training, most notably Art Cooper, MMC Board Chairman and Dolphins Plus Vice President and Curator. Funding for this work and Castaway’s care was provided by Dolphins Plus, Inc.</p>
<p><strong>References</strong></p>
<p>Belting, T., Joseph J., Messermith M. &amp; Nordone L. (1998) Teaching an old polar bear program new tricks. <em>Soundings 23</em>(2): 12-14</p>
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		<dc:creator>Bob</dc:creator>
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		<description><![CDATA[<a href="http://www.mmsc.org/">Marine Mammal Stranding Center</a>
<a href="http://www.marinemammalcenter.org/">The Marine Mammal Center</a>
<a href="http://www.rtis.com/nat/user/elsberry/marspec/pms_cet_spc.html">Online                Zoologists: Cetaceans</a>
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			<content:encoded><![CDATA[<p><a href="http://www.mmsc.org/">Marine Mammal Stranding Center</a></p>
<p><a href="http://www.marinemammalcenter.org/">The Marine Mammal Center</a></p>
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<p><a href="http://www.fau.edu/hboi">Harbor Branch</a></p>
<p><a href="http://www.mote.org">Mote Marine Laboratory</a></p>
<p><a href="http://www.swbg-conservationfund.org">Sea World Orlando</a></p>
<p><a href="http://www.ducks.org">Duck Unlimited</a></p>
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<p><a href="http://www.janegoodall.org">Jane Goodall Foundation</a></p>
<p><a href="http://www.nature.org">It&#8217;s The Nature Conservancy</a></p>
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		<pubDate>Tue, 27 Oct 2009 23:31:51 +0000</pubDate>
		<dc:creator>Bob</dc:creator>
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]]></description>
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<a href="http://www.dolphinscove.com/">Dolphin Cove</a><br />
<a href="http://www.islanddolphincare.org/">Island Dolphin Care</a></p>
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		<pubDate>Tue, 27 Oct 2009 23:28:59 +0000</pubDate>
		<dc:creator>Bob</dc:creator>
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Government Resources and Information
<strong>U S Fish &#38; Wildlife Service</strong> <a href="http://www.fws.gov/">http://www.fws.gov/</a>
The principal Federal Agency responsible for protecting endangered and threatened&#8230;]]></description>
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<p><strong>U S Fish &amp; Wildlife Service</strong> <a href="http://www.fws.gov/">http://www.fws.gov/</a><br />
The principal Federal Agency responsible for protecting endangered and threatened species and restoring them to a secure status in the wild is the primary objective of the endangered species program of the U.S. Fish and Wildlife Service, an agency of the Department of the Interior.</p>
<p><strong>National Marine Fisheries Service</strong> <a href="http://www.nmfs.noaa.gov/">http://www.nmfs.noaa.gov/</a><br />
The National Marine Fisheries Service administers NOAA&#8217;s programs which support the domestic and international conservation and management of living marine resources. NMFS provides services and products to support domestic and international fisheries management operations, fisheries development,, trade and industry assistance activities, enforcement, protected species and habitat conservation operations, and the scientific and technical aspects of NOAA&#8217;s marine fisheries program.</p>
<p><strong>Florida Fish &amp; Wildlife Conservation Commission; Bureau                of Protected Species Management</strong> <a href="http://myfwc.com/psm/">http://myfwc.com/psm/</a><br />
The Bureau of Protected Species Management (BPSM) is responsible for planning and implementing management activities directed towards the protection and recovery of manatees, other marine mammals (e.g., the endangered right whale), sea turtles and their essential habitats.</p>
<p><strong>National Oceanographic and Atmospheric Administration</strong> <a href="http://www.noaa.gov/">http://www.noaa.gov/</a><br />
NOAA warns of dangerous weather, charts our seas and skies, guides our use and protection of ocean and coastal resources, and conducts research to improve our understanding and stewardship of the environment which sustains us all.</p>
<p><strong>United Nations Ocean Affairs and Law of the Sea</strong> <a href="http://www.un.org/Depts/los/">http://www.un.org/Depts/los/</a><br />
The United Nations Convention on the Law of the Sea is the third in a series of United Nations efforts to codify the rules by which nations utilize over 70% of the earth&#8217;s surface. All aspects of the use of the oceans, from the edge of the coast to the bottom of the deepest sea are addressed in this convention. Over three hundred articles in length, this is perhaps the most complex legal agreement ever achieved.</p>
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		<pubDate>Tue, 27 Oct 2009 21:56:38 +0000</pubDate>
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		<description><![CDATA[<strong> </strong>

<strong>Robin B. Friday, Sr.</strong>
Robin Friday is the founder of Wildlife International Network and serves as the Chairman of the Board and Chief Executive Officer of Ocean Embassy, Inc. and Wi&#8230;]]></description>
			<content:encoded><![CDATA[<p align="center"><strong> </strong></p>
<p align="center">
<p align="center"><strong>Robin B. Friday, Sr.</strong></p>
<p>Robin Friday is the founder of Wildlife International Network and serves as the Chairman of the Board and Chief Executive Officer of Ocean Embassy, Inc. and Wildlife International Network, Inc.  Beginning his marine mammal experience at the SeaWorld parks, Robin Friday held positions as Curator and Director of the Animal Training, Aviculture, and Animal Care departments over a period of 18 years.  He also led the development of Discovery Cove, Orlando (a $121 US million dollar dolphin interaction facility built by Busch Entertainment Corp.). Following his SeaWorld tenure, Friday served as General Manager of Marineland Foundation, Inc., a 501©(3) corporation, where he designed and implemented a dolphin interaction program. As Project Manager for Ocean Futures Society (OFS &#8211; Jean-Michele Cousteau Institute) he led a special project team from 1998 to 2000 to rehabilitate Keiko the killer whale, of “Free Willy” fame. Milestones achieved while managing the Keiko project included: strategic reorganization of project objectives and organizational structure on site in Vestmannaeyjar, Iceland; construction of an 800 ft. barrier net across Klettsvik Bay, Iceland; development of regulatory and protocol guidelines which resulted in the Icelandic government awarding release permits to OFS; and completion of the world’s first successful open-ocean behavioral conditioning of a captive killer whale. Friday also managed the development of the world’s first marine mammal teaching hospital for the Marine Mammal Research and Conservation Department at Harbor Branch Oceanographic Institute in Ft. Pierce, Florida, a $26 million expansion. Responsibilities included: implementing government regulatory requirements, overseeing operational budgets, staff management and support of the Southeast Stranding Network.</p>
<p align="center"><strong>Mark A. Simmons</strong></p>
<p>Mark Simmons is one of the founders of the Company and currently the Secretary/Treasurer of the Board and Executive Vice President for Ocean Embassy, Inc. and Wildlife International Network, Inc. (parent company of Ocean Embassy). Mark has been working with founder, Robin Friday for 16 years and has worked in the marine mammal industry for more than 18 years. He specialized in marine mammal behavioral sciences throughout ten years of employment with SeaWorld of Florida. While there, he also was responsible for over $21 US million in animal assets, assisted in the development of approximately three multi-million dollar animal facilities and represented SeaWorld via speaking engagements both locally and abroad. Simmons and Friday also teamed up at Marineland, developing a dolphin interaction program, and in Iceland managing, the Keiko Reintroduction Project for Ocean Futures Society (“OFS”). Well experienced in the design, implementation and operation of all types of marine mammal public display programs, he participated in creating marine mammal shows, educational curriculum, research and interactive programs. Simmons also has extensive experience in regulatory compliance both with the United States and foreign governments.</p>
<p align="center"><strong>Ted N. Turner</strong></p>
<p>In his role as VP of International Operations, Ted Turner oversees and manages all aspects of government and international regulation, legislation and permitting. Ted also monitors all international treaties and agreements pertaining to marine mammal and marine species trade and regulatory guidelines. He is among the most knowledgeable professionals in the area of behavioral sciences, international marine mammal laws and treaties, regulatory development and zoological research, public display and education. In addition, Ted leads the Company in concept development and has innovated some of the most exciting new facility and program concepts proposed in the industry.</p>
<p>A senior zoological executive with over 20 years of marine life management experience, Turner held the position of Vice President/Curator of Animal Training for SeaWorld Ohio for over nine years. As a senior member of the executive team, He also served as a member of Busch Entertainment Corporation’s New Product Development Team and Corporate Behavior Review Committee and was named Corporate Coordinator for SeaWorld Animal Training Research. Between 1988 and 2000, he authored and implemented a comprehensive and intense staff training program designed for Discovery Cove, Orlando, which was instrumental in the successful opening of this new theme park in the summer of 2000. Turner also developed five animal interactive programs as well as the initial animal design concept for Discovery Cove, Atlantis in The Bahamas and the United Arab Emirates. He has authored over 40 articles on animal management including book chapters for Smithsonian and Academic Press on the subject of behavior modification and enrichment for marine mammals. In addition he has given numerous lectures as an invited guest speaker for groups such as the Ohio Veterinary Medical Association (Columbus, Ohio), the Great Plains Student Psychology Conference (Joplin, Missouri), the International Whale Symposium (San Diego, California), and State University of New York (Binghamton, New York) among others. Turner served as President of the International Marine Mammal Trainers Association (IMATA), an NGO representative for the Convention on the International Trade in Endangered Species (CITES – Kyoto Japan) and continues to help governments develop international legislation for the protection of marine mammals.</p>
<p align="center"><strong>Todd R. Feucht</strong></p>
<p>Todd Feucht is a zoological professional with over 17 years of specialized marine mammal management and business development experience. Todd currently holds the position of Vice President of Ocean Embassy and is a Professional member of the International Marine Animal Trainers Association (IMATA). In this integral leadership position, Todd is involved in all aspects of the Company’s objectives and provides business oversight and represents the Company in analyzing new growth opportunities.</p>
<p>Mr. Feucht began his career with Busch Entertainment Corporation (BEC) in 1990 at SeaWorld Ohio and developed a comprehensive knowledge of advanced behavior modification techniques, aggression management and behavioral medicine. He has held supervisory positions with both SeaWorld Ohio and SeaWorld Orlando where he was responsible for animal management, show production and quality, staff management, staff development, safety and guest interactive programs. During his tenure with SeaWorld, Feucht was involved with the training and management of killer whales (<em>Orcinus orca</em>), Pacific white-sided dolphins (<em>Lagenorynchus obliquidens</em>), Commerson’s dolphins (<em>Cephalorhynchus commersonii</em>), bottlenose dolphins (<em>Tursiops truncates)</em>, false killer whales (<em>Pseudorca crassidens</em>), and California Sea Lions (<em>Zalophus californianus</em>). While with SeaWorld, he was also involved with numerous complex and high profile animal transports with a variety of animal species, including killer whales, Pacific white-sided dolphins, Commerson’s dolphins, and bottlenose dolphins.</p>
<p>In 1998, Mr. Feucht was recruited by Sea Life Park Hawaii to design and implement their first and only fully submersive dolphin swim experience (Dolphin Adventure), a highly successful interactive program. While in Hawaii, Feucht also led the development of program design, product improvement and behavioral protocols for the dolphin interaction program at the Kahala Manderin Oriental Hotel, located on Oahu.</p>
<p>Mr. Feucht has been involved with many other aspects of marine mammal animal management including field work, facility design, program feasibility and marine mammal research/data collection. He has been an invited speaker at animal behavior seminars throughout the United States and Europe and has helped develop marine mammal protection legislation for foreign governments including Panama, The Bahamas, United Arab Emirates and St. Lucia.</p>
<p align="center"><strong>Mark Andrew Trimm</strong></p>
<p>Mark Trimm has been with Ocean Embassy since late in 2004. Mark manages all aspects of facility development for the Company as well as zoological logistics and husbandry programs. His experience has made him one of the most knowledgeable professionals in marine zoological facility design, construction and operation. Mark is also one of few individuals in the industry with an extensive background in marine mammal rescue and rehabilitation. In this capacity, he has developed procedures and protocols for the Company’s rescue and rehabilitation programs including research and educational components.</p>
<p>Mark has worked in the Marine Mammal field for the last 22 years around the world and has managed both large and small collections of marine mammals. He has worked in varying capacities with no less than twenty-eight different species of marine mammals and dozens of Terrestrial species from all over the world. His expertise includes the following areas:</p>
<p>• Animal Care &amp; Husbandry.<br />
• Animal Management.<br />
• Medical Supportive Care.<br />
• Marine Mammal Rescue, Rehabilitation &amp; Release.<br />
• Manage Field Research / Animal Documentary Filming.<br />
• Marine Mammal Collection<br />
• Marine Mammal Transport &amp; Complex Logistics Planning<br />
• Operant Conditioning<br />
• College Level Instructor, Credited Course Work On Marine Mammals<br />
• Captive Propagation<br />
• Specialized Marine Mammal Equipment Design<br />
• Facility, Hospital, Exhibit Design &amp; Operation<br />
• Facility Start-Up</p>
<p>Mr. Trimm has contributed to numerous technical and medical publications on marine mammals relating to both wild animals and animals under the care of humans. He is sought for his expertise in multiple areas such as conducting talks about marine mammals to all age groups as well as assist the U. S. National Marine Fisheries Department put on Necropsy Workshops for members of the Southeast Stranding Network. He participates in annual Level “A” field research health assessments on free ranging pods of bottlenose dolphins in two different states in the United States and instructs in the proper handling of animals during and following the capture process. Mark has managed every aspect of Marine Mammal rescue of well over one hundred stranded marine mammals. He has supervised the treatment during the rehabilitation process and successfully released and tracked dozens of Whales Dolphins and Manatees back to the wild.</p>
<p style="text-align: center;"><strong> Dr. Stan Kuczaj</strong></p>
<p>Dr. Stan Kuczaj is an expert in the field of comparative psychology, with an emphasis on marine mammal behavior, cognition, and communication. His current work focuses on the ontogeny and organization of social behavior (including communication) in cetaceans, the assessment of personality in nonhuman animals, the effects of anthropogenic noise on marine mammals, and problem solving in dolphins, sea lions and whales.  Dr. Kuczaj is a founding fellow of the Association for Psychological Science, a founding member of the Comparative Cognition Society, and a fellow of the American Psychological Association. He is also a member of numerous professional organizations, including the Acoustical Society of America, the Animal Behavior Society, the European Association for Aquatic Mammals, and the Society for Marine Mammalogy.</p>
<p>Dr. Kuczaj won a Young Scientist Award from the American Psychological Association for his work on child language development, and an Excellence in Basic Research Award from the University of Southern Mississippi for his research on dolphin cognition and behavior.  He is the faculty advisor for the Gulf Coast student chapter of the Society for Marine Mammalogy, and is Editor of the <em>International Journal of Comparative Psychology </em>and Associate Editor of <em>First Language. </em> In addition to his role at MMC, he serves on the Advisory Boards of the Dolphin Communication Project and the Institute for Marine Mammal Studies, the Scientific Advisory Board for the Wild Dolphin Project, and the Scientific Committees of Gulf World Oceanarium and the European Association for Aquatic Mammals.</p>
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		<title>MMC Research Committee</title>
		<link>http://marinemammalconservancy.org/research/mmc-research-committee</link>
		<comments>http://marinemammalconservancy.org/research/mmc-research-committee#comments</comments>
		<pubDate>Tue, 27 Oct 2009 21:27:03 +0000</pubDate>
		<dc:creator>Bob</dc:creator>
				<category><![CDATA[Contact the Research Committee]]></category>
		<category><![CDATA[Research]]></category>

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		<description><![CDATA[<strong>Chairman Art Cooper   <a href="mailto:Art@marinemammalconservancy.org">Art@marinemammalconservancy.org</a></strong>
A senior marine mammal facility executive with over 20 years of experience, Cooper holds the position of Vice President&#8230;]]></description>
			<content:encoded><![CDATA[<p><strong>Chairman Art Cooper   <a href="mailto:Art@marinemammalconservancy.org">Art@marinemammalconservancy.org</a></strong></p>
<p>A senior marine mammal facility executive with over 20 years of experience, Cooper holds the position of Vice President/Curator of Dolphins Plus Key Largo, responsible for $15 US million in animal assets.  Cooper developed and manages all animal in water interactions for Island Dolphin Care (IDC), a not for profit Key  Largo based organization working primarily with special needs children and at risk individuals.  He also holds the Curator position of Dolphin Cove Key Largo, $3 million in animal assets.  He was instrumental in the creation and development of Dolphin Resorts Tortola, BVI in conjunction with Prospect Reef Resort in 2001 where he served as program director and Curator, $4 million in animal assets.  In 2003, Cooper assisted in the planning and development of Dolphin Resorts Dominica, WI, where he served as Director of Operations and Curator, $4 million in animal assets.</p>
<p>Cooper is the Vice Chairman of The Marine Mammal Conservancy (MMC), a not for profit marine mammal rescue organization based in Key Largo, FL.  He served as Chairman from 2004 till 2009.  He serves as the Chairman of the Scientific, Research and Review Committee and is an Executive Board Member.  Cooper has been responsible for creating a world class Independent Advisory Group made up of marine mammal veterinarians, facility planners and managers, and the top marine mammal researchers.   Cooper was the long time President of the Marine Mammal Rescue Foundation of the Upper Keys and a board member of MMRF since 1990.  He has also held a personal Letter of Authorization from the National Marine Fisheries Service (NMFS) to conduct stranding activities regarding marine mammals in US waters.</p>
<p>Cooper is experienced in marine mammal husbandry, rescue, emergency medical care, animal acquisition, facility design, development, and operation.  His responsibilities include: local and international transports, animal enclosure development and maintenance, education of animal care, husbandry, and training staff, facilitating insurance for all in-water programs, program development, all human resources, implementing regulatory requirements, maintaining husbandry standards, and ensuring a positive working environment for staff and animals.</p>
<p><strong>Dr. Robert O. Stevens    <a href="mailto:DrStevens@marinemammalconservancy.org">DrStevens@marinemammalconservancy.org</a></strong><br />
<strong> </strong></p>
<p>Dr. Robert O. Stevens<strong> </strong>graduated from the College of Veterinary Medicine at Auburn University, in 1975. Dr. Stevens worked in private practice with Dr. Deke Beusse, prior to joining the veterinary team as Staff Veterinarian and Assistant Curator of Mammal and Birds at Sea World Ohio, in 1977. In 1985, Dr. Stevens established the Mobile Veterinary Clinic, a private exotic and small animal practice. Around the same time, he became the contract veterinarian for Epcot’s then-newly constructed Living Seas Pavilion. Dr. Stevens is currently the Director of Animal Health Services at Dolphins Plus and Dolphin Cove and is the Veterinarian of Record for MMC. Dr. Stevens’ has worked with a wide range of exotic animals, from marine mammals, birds, fish and reptiles to both small and large species of domestic animals.</p>
<p><strong>Dr. Micah C. Brodsky   <a href="mailto:DrBrodsky@marinemammalconservancy.org">DrBrodsky@marinemammalconservancy.org</a></strong></p>
<p>Dr. Micah C. Brodsky graduated from the University Of Pennsylvania School Of Veterinary Medicine, in 2002. Since then, he has been involved with a number of different projects as a consulting veterinarian, including the Olive Ridley Sea Turtle Research Project at the La Flor Wildlife Refuge in Paya La Flor, Rivas, Nicaragua. He has also worked on the Wild Dolphin Health and Risk Assessment Program at the Harbor Branch Oceanographic Institution, as well as the Marine Mammal Health Assessment, Sirenia Project regarding manatee biology, ecology and adaptive management in the south Florida area. He has worked primarily with wildlife and continues to work and volunteer time for a variety of domestic and international conservation projects. Dr. Brodsky is currently staff veterinarian for Dolphins Plus and Dolphin Cove and consulting veterinarian for MMC. Dr. Brodsky’s professional interests include clinical medicine, conservation medicine and epidemiology.</p>
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		<title>Environmental Impact</title>
		<link>http://marinemammalconservancy.org/research/environmental-impact</link>
		<comments>http://marinemammalconservancy.org/research/environmental-impact#comments</comments>
		<pubDate>Thu, 20 Aug 2009 22:32:51 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Other Organizations]]></category>
		<category><![CDATA[Research]]></category>

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		<description><![CDATA[NOAA Fisheries requirements state that no marine mammal shall                be released back into the wild without first being certified healthy                and a non-danger to existing populations. Tha&#8230;]]></description>
			<content:encoded><![CDATA[<p style="text-align: center;"><img class="aligncenter size-full wp-image-565" title="NOAA Dolphin Photo 2" src="http://mmc.coedmediagroup.com/wp-content/uploads/2009/10/NOAA-Dolphin-Photo-2.jpg" alt="NOAA Dolphin Photo 2" width="480" height="360" />NOAA Fisheries requirements state that no marine mammal shall                be released back into the wild without first being certified healthy                and a non-danger to existing populations. That process involves                the review of medical records by seventeen (17) marine mammal veterinarians                and a permit by NOAA Fisheries. The Marine Mammal Conservancy also                insures that release candidates are able to capture their own food                and are desensitized to human contact as part of our own release                protocols.</p>
<p><strong>Abbreviations:</strong></p>
<p>Personal:<br />
DVM: Doctor of Veterinary Medicine<br />
VMD: Veterinary Medical Doctor</p>
<p>Organizations:<br />
FDEP: Florida Department of Environmental Protection<br />
FMP: Florida Marine Patrol<br />
MMC: Marine Mammal Conservancy<br />
MMRF: Marine Mammal Rescue Foundation of the Upper Keys<br />
WRFK: Wildlife Rescue of the Florida Keys<br />
MARS: Marine Animal Rescue Society<br />
DRC: Dolphin Research Center<br />
MMSC: Marine Mammal Stranding Center in Brigantine, New Jersey<br />
NMFS: National Marine Fisheries Service<br />
UM: University of Miami Pathology Lab located at the Jackson Memorial                Hospital Complex in Miami Florida</p>
<p>General:<br />
LOA: Letter of Agreement issued to organizations by the National                Marine Fisheries Service<br />
MM: Mile Marker; The easiest most effective way to identify locations                in the Florida Keys. The mile markers are referenced along the Overseas                Highway.</p>
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