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								<c val="#008080">SIGNAL PROCESSING EXTENSION PACK</c>
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				<phrase>signal processing extension pack</phrase>
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								<c val="#008080">About This Extension Pack</c>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">The <f family="Times New Roman" charset="0">
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					</f> is a collection of 76 useful signal processing functions. Once you have installed the extra functions that come with this extension pack, they are available whenever you run <f family="Times New Roman" charset="0">
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				<phrase>functions, signal processing</phrase>
				<phrase>signal processing functions</phrase>
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		<region region-id="32" left="6" top="162.75" width="295.5" height="57" align-x="6" align-y="174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">The quickest way to get to know the Signal Pack is to browse through this E-book. The <b>
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							<link href="./Index.xmcd" title="Links to section" popup="false">index</link>
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					</b> lists all the functions, and each function name is hyperlinked to a document that describes that function and usually some related functions as well. </p>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">When a document discusses several functions, the page where the information on each function begins is shown at the top of the document. Some documents contain 10 or 20 screens, so be sure to scroll down to see all the information on the functions discussed. </p>
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		<region region-id="35" left="6" top="312.75" width="279" height="28.5" align-x="6" align-y="324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Here are some points to remember when you use these signal processing functions:</p>
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						<b>
							<c val="#008080">• </c>
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					</f>You don't need to have this E-book open to use the signal processing functions. They are available as soon as you install the extra functions.</p>
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		<region region-id="196" left="6" top="396" width="282" height="72" align-x="6" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
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						<b>
							<c val="#008080">• </c>
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					</f>All functions in this pack require dimensionless arguments; don't use arguments that have units attached. Frequency is generally measured in Hertz-seconds, that is, as a fraction of the sampling frequency. Frequency arguments are thus typically between 0 and 0.5. </p>
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			<indexes>
				<phrase>units</phrase>
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		<region region-id="197" left="6" top="474" width="303.75" height="29.25" align-x="6" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
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						<b>
							<c val="#008080">• </c>
						</b>
					</f>We use <f family="Times New Roman" charset="0">
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					</f> default numbering for arrays throughout this E-book, with the first element having index 0.</p>
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				<phrase>arrays</phrase>
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		<region region-id="198" left="6" top="510" width="302.25" height="201" align-x="6" align-y="522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
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						<b>
							<c val="#008080">• </c>
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					</f>Many of the signal processing functions are based on the discrete Fourier transform and make use of <f family="Times New Roman" charset="0">
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					</f> built-in FFT routine. In order to provide maximum flexibility, we have not restricted the lengths of input arrays to powers of 2. But note that when a long input vector has a length with only one or two factors, the FFT routine will be slow. (In the extreme case in which the length is a large prime, the FFT can do no better than add up the exponential sums that define the transform.) Thus a small change in the length can make a big difference in computation time. Compare the computation of CFFT for a vector of length 5000 and one of length 4999. Note that CFFT implements the standard definition of the discrete Fourier transform, in which the forward transform uses the kernel <b>exp</b>
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			<indexes>
				<phrase>FFTs</phrase>
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						<b>
							<c val="#008080">• </c>
						</b>
					</f>Many of the functions in this pack have restrictions on their arguments. For example, most of the transform and correlation functions work only on real input vectors, and the sine and cosine transforms require arguments of even length. See the E-book sections on the individual functions for details. </p>
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		<region region-id="55" left="0" top="798" width="6000" height="6" align-x="0" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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		<region region-id="56" left="6" top="810.75" width="165.75" height="14.25" align-x="6" align-y="822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Times New Roman" charset="0">
						<b>
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								<c val="#800000">A Signal Processing Bibliography</c>
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			<indexes>
				<phrase>signal processing bibliography</phrase>
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		<region region-id="57" left="6" top="828.75" width="278.25" height="42.75" align-x="6" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">The functions in this pack implement methods and algorithms described in the following books, which are good sources for further background on signal processing.</p>
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		</region>
		<region region-id="58" left="6" top="882.75" width="276" height="28.5" align-x="6" align-y="894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Bruce L. Bowerman and Richard T. O'Connell, <i>Time Series Forecasting</i>, Duxbury Press (1987).</p>
			</text>
		</region>
		<region region-id="59" left="6" top="918.75" width="302.25" height="28.5" align-x="6" align-y="930" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Ronald N. Bracewell, <i>The Hartley Transform</i>, Oxford University Press (1986).</p>
			</text>
		</region>
		<region region-id="167" left="6" top="954.75" width="291.75" height="14.25" align-x="6" align-y="966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Leon Cohen, <f family="Times New Roman" charset="0">
						<i>
							<inlineAttr line-through="false">Time-Frequency Analysis</inlineAttr>
						</i>
					</f>, Prentice-Hall (1995).</p>
			</text>
		</region>
		<region region-id="60" left="6" top="978.75" width="291.75" height="28.5" align-x="6" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Rafael C. Gonzalez and Paul Wintz, <i>Digital Image Processing</i>, Addison-Wesley (1977).</p>
			</text>
		</region>
		<region region-id="61" left="6" top="1014.75" width="284.25" height="28.5" align-x="6" align-y="1026" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">C. W. J. Granger and Paul Newbold, <i>Forecasting Economic Time Series</i>, Academic Press, Inc. (1986).</p>
			</text>
		</region>
		<region region-id="164" left="6" top="1050.75" width="291" height="28.5" align-x="6" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Hwei P. Hsu, <f family="Times New Roman" charset="0">
						<i>
							<inlineAttr line-through="false">Schaum's Outline of Theory and Programming of Signals and Systems</inlineAttr>
						</i>
					</f>, McGraw-Hill, Inc.(1995). </p>
			</text>
		</region>
		<region region-id="62" left="6" top="1092.75" width="262.5" height="28.5" align-x="6" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">S. Lawrence Marple, Jr., <i>Digital Spectral Analysis with Applications</i>, Prentice-Hall (1987).</p>
			</text>
		</region>
		<region region-id="63" left="6" top="1128.75" width="279.75" height="28.5" align-x="6" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Sophocles J. Orfanidis, <i>Optimum Signal Processing</i>, 2d ed, Macmillan (1988).</p>
			</text>
		</region>
		<region region-id="64" left="6" top="1164.75" width="246.75" height="28.5" align-x="6" align-y="1176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">T. W. Parks and C. S. Burrus, <i>Digital Filter Design</i>, Wiley-Interscience (1987).</p>
			</text>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Alan V. Oppenheim and Ronald W. Schafer, <f family="Times New Roman" charset="0">
						<i>
							<inlineAttr line-through="false">Discrete-Time Signal Processing,</inlineAttr>
						</i>
					</f> Prentice Hall (1989).</p>
			</text>
		</region>
		<region region-id="169" left="6" top="1242.75" width="264" height="42.75" align-x="6" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Donald B. Percival and Andrew T. Walden, <f family="Times New Roman" charset="0">
						<i>
							<inlineAttr line-through="false">Spectral Analysis of Physical Applications</inlineAttr>
						</i>
					</f>, Cambridge University Press (1993).</p>
			</text>
		</region>
		<region region-id="65" left="6" top="1296.75" width="276" height="42.75" align-x="6" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling, <i>Numerical Recipes in C</i>, Cambridge University Press (1988).</p>
			</text>
		</region>
		<region region-id="66" left="6" top="1350.75" width="285" height="14.25" align-x="6" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<i>Programs for Digital Signal Processing</i>, IEEE Press (1979).</p>
			</text>
		</region>
		<region region-id="67" left="6" top="1374.75" width="303.75" height="28.5" align-x="6" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Lawrence R. Rabiner and Bernard Gold, <i>Theory and Application of Digital Signal Processing</i>, Prentice-Hall, Inc. (1975).</p>
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		<region region-id="68" left="6" top="1410.75" width="300" height="28.5" align-x="6" align-y="1422" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Mary Beth Ruskai et al., eds., <i>Wavelets and Their Applications</i>, Jones and Bartlett Publishers (1992).</p>
			</text>
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		<region region-id="69" left="6" top="1446.75" width="311.25" height="28.5" align-x="6" align-y="1458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Samuel Stearns and Ruth A. David, <i>Signal Processing Algorithms</i>, Prentice-Hall, Inc. (1988).</p>
			</text>
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