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<span class="path"><a href="index.html">FOSSEE Signal Processing Toolbox</a> >> <a href="section_5118e822ecc2888aa80042108de4932e.html">FOSSEE Signal Processing Toolbox</a> > peig</span>
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<span class="path"><a href="index.html">FOSSEE Signal Processing Toolbox</a> >> <a href="section_cc2bc01c47967d47fcf3507a91d572ba.html">FOSSEE Signal Processing Toolbox</a> > peig</span>
>>>>>>> 3f916032cc0b2efdeafb838dd10e1141ead2cb27
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<div class="refnamediv"><h1 class="refname">peig</h1>
<p class="refpurpose">Psuedospectrum using the eigenvector method.</p></div>
<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3>
<div class="synopsis"><pre><span class="default">[</span><span class="default">S</span><span class="default">,</span><span class="default">w</span><span class="default">] = </span><span class="functionid">peig</span><span class="default">(</span><span class="default">x</span><span class="default">,</span><span class="default">p</span><span class="default">)</span>
<span class="default">[</span><span class="default">S</span><span class="default">,</span><span class="default">w</span><span class="default">] = </span><span class="functionid">peig</span><span class="default">(</span><span class="default">x</span><span class="default">,</span><span class="default">p</span><span class="default">,</span><span class="default">w</span><span class="default">)</span>
<span class="default">[</span><span class="default">S</span><span class="default">,</span><span class="default">w</span><span class="default">] = </span><span class="functionid">peig</span><span class="default">(</span><span class="default">x</span><span class="default">,</span><span class="default">p</span><span class="default">,</span><span class="default">nfft</span><span class="default">)</span>
<span class="default">[</span><span class="default">S</span><span class="default">,</span><span class="default">w</span><span class="default">] = </span><span class="functionid">peig</span><span class="default">(</span><span class="default">x</span><span class="default">,</span><span class="default">p</span><span class="default">,</span><span class="default">nfft</span><span class="default">,</span><span class="default">fs</span><span class="default">)</span>
<span class="default">[</span><span class="default">S</span><span class="default">,</span><span class="default">w</span><span class="default">] = </span><span class="functionid">peig</span><span class="default">(</span><span class="default">x</span><span class="default">,</span><span class="default">p</span><span class="default">,</span><span class="default">f</span><span class="default">,</span><span class="default">fs</span><span class="default">)</span>
<span class="default">[</span><span class="default">S</span><span class="default">,</span><span class="default">f</span><span class="default">] = </span><span class="functionid">peig</span><span class="default">(...,</span>'<span class="default">corr</span>'<span class="default">)</span>
<span class="default">[</span><span class="default">S</span><span class="default">,</span><span class="default">f</span><span class="default">] = </span><span class="functionid">peig</span><span class="default">(</span><span class="default">x</span><span class="default">,</span><span class="default">p</span><span class="default">,</span><span class="default">nfft</span><span class="default">,</span><span class="default">fs</span><span class="default">,</span><span class="default">nwin</span><span class="default">,</span><span class="default">noverlap</span><span class="default">)</span>
<span class="default">[...] = </span><span class="functionid">peig</span><span class="default">(...,</span><span class="default">freqrange</span><span class="default">)</span>
<span class="default">[...,</span><span class="default">v</span><span class="default">,</span><span class="default">e</span><span class="default">] = </span><span class="functionid">peig</span><span class="default">(...)</span>
<span class="default">Parameters</span><span class="default">:</span>
<span class="default">x</span><span class="default"> - </span><span class="default">int</span><span class="default">|</span><span class="default">double</span><span class="default"> - </span><span class="default">vector</span><span class="default">|</span><span class="default">matrix</span>
<span class="default">Input</span> <span class="default">signal</span><span class="default">. </span><span class="default">In</span> <span class="default">case</span> <span class="default">of</span> <span class="default">a</span> <span class="default">matrix</span><span class="default">, </span><span class="default">each</span> <span class="default">row</span> <span class="default">of</span> <span class="default">x</span> <span class="default">represents</span> <span class="default">a</span>
<span class="default">seperate</span> <span class="default">observation</span> <span class="default">of</span> <span class="default">the</span> <span class="default">signal</span><span class="default">. </span><span class="default">If</span> '<span class="default">corr</span>' <span class="default">flag</span> <span class="default">is</span> <span class="default">specified</span><span class="default">,</span>
<span class="default">then</span> <span class="default">x</span> <span class="default">is</span> <span class="default">the</span> <span class="default">correlation</span> <span class="default">matrix</span><span class="default">.</span>
<span class="default">If</span> <span class="default">w</span> <span class="default">is</span> <span class="default">not</span> <span class="default">specified</span> <span class="default">in</span> <span class="default">the</span> <span class="default">input</span><span class="default">, </span><span class="default">it</span> <span class="default">is</span> <span class="default">determined</span> <span class="default">by</span> <span class="default">the</span>
<span class="default">algorithm</span><span class="default">. </span><span class="default">If</span> <span class="default">x</span> <span class="default">is</span> <span class="default">real</span> <span class="default">valued</span><span class="default">, </span><span class="default">then</span> <span class="default">range</span> <span class="default">of</span> <span class="default">w</span> <span class="default">is</span><span class="default"> [0, </span><span class="default">pi</span><span class="default">].</span>
<span class="default">Otherwise</span><span class="default">, </span><span class="default">the</span> <span class="default">range</span> <span class="default">of</span> <span class="default">w</span> <span class="default">is</span><span class="default"> [0, 2</span><span class="default">pi</span><span class="default">)</span>
<span class="default">p</span><span class="default"> - </span><span class="default">int</span><span class="default">|</span><span class="default">double</span><span class="default"> - </span><span class="default">scalar</span><span class="default">|</span><span class="default">vector</span>
<span class="default">p</span><span class="default">(1) </span><span class="default">is</span> <span class="default">the</span> <span class="default">dimension</span> <span class="default">of</span> <span class="default">the</span> <span class="default">signal</span> <span class="default">subspace</span>
<span class="default">p</span><span class="default">(2), </span><span class="default">if</span> <span class="default">specified</span><span class="default">, </span><span class="default">represents</span> <span class="default">a</span> <span class="default">threshold</span> <span class="default">that</span> <span class="default">is</span> <span class="default">multiplied</span> <span class="default">by</span>
<span class="default">the</span> <span class="default">smallest</span> <span class="default">estimated</span> <span class="default">eigenvalue</span> <span class="default">of</span> <span class="default">the</span> <span class="default">signal</span>'<span class="default">s</span> <span class="default">correlation</span> <span class="default">matrix</span><span class="default">.</span>
<span class="default">w</span><span class="default"> - </span><span class="default">int</span><span class="default">|</span><span class="default">double</span><span class="default"> - </span><span class="default">vector</span>
<span class="default">w</span> <span class="default">is</span> <span class="default">the</span> <span class="default">vector</span> <span class="default">of</span> <span class="default">normalized</span> <span class="default">frequencies</span> <span class="default">over</span> <span class="default">which</span> <span class="default">the</span>
<span class="default">pseuspectrogram</span> <span class="default">is</span> <span class="default">to</span> <span class="default">be</span> <span class="default">computed</span><span class="default">.</span>
<span class="default">nfft</span><span class="default"> - </span><span class="default">int</span><span class="default"> - </span><span class="default">scalar</span><span class="default"> (</span><span class="default">Default</span><span class="default"> = 256)</span>
<span class="default">Length</span> <span class="default">of</span> <span class="default">the</span> <span class="default">fft</span> <span class="default">used</span> <span class="default">to</span> <span class="default">compute</span> <span class="default">pseudospectrum</span><span class="default">. </span><span class="default">The</span> <span class="default">length</span> <span class="default">of</span> <span class="default">S</span>
<span class="default">(</span><span class="default">and</span> <span class="default">hence</span> <span class="default">w</span><span class="default">/</span><span class="default">f</span><span class="default">) </span><span class="default">depends</span> <span class="default">on</span> <span class="default">the</span> <span class="default">type</span> <span class="default">of</span> <span class="default">values</span> <span class="default">in</span> <span class="default">x</span> <span class="default">and</span> <span class="default">nfft</span><span class="default">.</span>
<span class="default">If</span> <span class="default">x</span> <span class="default">is</span> <span class="default">real</span><span class="default">, </span><span class="default">length</span> <span class="default">of</span> <span class="default">s</span> <span class="default">is</span><span class="default"> (</span><span class="default">nfft</span><span class="default">/</span><span class="default">2 + 1) {</span><span class="default">Range</span> <span class="default">of</span> <span class="default">w</span><span class="default"> = [0, </span><span class="default">pi</span><span class="default">]} </span><span class="default">if</span>
<span class="default">nfft</span> <span class="default">is</span> <span class="default">even</span> <span class="default">and</span><span class="default"> (</span><span class="default">nfft</span><span class="default">+1)</span><span class="default">/</span><span class="default">2 {</span><span class="default">Range</span> <span class="default">of</span> <span class="default">w</span><span class="default"> = [0, </span><span class="default">pi</span><span class="default">)} </span><span class="default">otherwise</span><span class="default">.</span>
<span class="default">If</span> <span class="default">x</span> <span class="default">is</span> <span class="default">complex</span><span class="default">, </span><span class="default">length</span> <span class="default">of</span> <span class="default">s</span> <span class="default">is</span> <span class="default">nfft</span><span class="default">.</span>
<span class="default">fs</span><span class="default"> - </span><span class="default">int</span><span class="default">|</span><span class="default">double</span><span class="default"> - </span><span class="default">scalar</span><span class="default"> (</span><span class="default">Default</span><span class="default"> = 1)</span>
<span class="default">Sampling</span> <span class="default">rate</span><span class="default">. </span><span class="default">Used</span> <span class="default">to</span> <span class="default">convert</span> <span class="default">the</span> <span class="default">normalized</span> <span class="default">frequencies</span><span class="default"> (</span><span class="default">w</span><span class="default">) </span><span class="default">to</span>
<span class="default">actual</span> <span class="default">values</span><span class="default"> (</span><span class="default">f</span><span class="default">) </span><span class="default">and</span> <span class="default">vice</span><span class="default">-</span><span class="default">versa</span><span class="default">.</span>
<span class="default">nwin</span><span class="default"> - </span><span class="default">int</span><span class="default">|</span><span class="default">double</span><span class="default"> - </span><span class="default">scalar</span><span class="default"> (</span><span class="default">int</span> <span class="default">only</span><span class="default">)|</span><span class="default">vector</span><span class="default"> (</span><span class="default">Default</span><span class="default"> = 2*</span><span class="default">p</span><span class="default">(1))</span>
<span class="default">If</span> <span class="default">nwin</span> <span class="default">is</span> <span class="default">scalar</span><span class="default">, </span><span class="default">it</span> <span class="default">is</span> <span class="default">the</span> <span class="default">length</span> <span class="default">of</span> <span class="default">the</span> <span class="default">rectangular</span> <span class="default">window</span><span class="default">.</span>
<span class="default">Otherwise</span><span class="default">, </span><span class="default">the</span> <span class="default">vector</span> <span class="default">input</span> <span class="default">is</span> <span class="default">considered</span> <span class="default">as</span> <span class="default">the</span> <span class="default">window</span> <span class="default">coefficients</span><span class="default">.</span>
<span class="default">Not</span> <span class="default">used</span> <span class="default">if</span> '<span class="default">corr</span>' <span class="default">flag</span> <span class="default">present</span><span class="default">.</span>
<span class="default">If</span> <span class="default">x</span> <span class="default">is</span> <span class="default">a</span> <span class="default">vector</span><span class="default">, </span><span class="default">windowing</span> <span class="default">not</span> <span class="default">done</span> <span class="default">in</span> <span class="default">nwin</span> <span class="default">in</span> <span class="default">scalar</span><span class="default">. </span><span class="default">If</span> <span class="default">x</span> <span class="default">is</span> <span class="default">a</span>
<span class="default">matrix</span><span class="default">,</span>
<span class="default">noverlap</span><span class="default"> - </span><span class="default">int</span><span class="default"> - </span><span class="default">scalar</span><span class="default"> (</span><span class="default">Default</span><span class="default"> = </span><span class="default">nwin</span><span class="default">-1)</span>
<span class="default">number</span> <span class="default">of</span> <span class="default">points</span> <span class="default">by</span> <span class="default">which</span> <span class="default">successive</span> <span class="default">windows</span> <span class="default">overlap</span><span class="default">. </span><span class="default">noverlap</span> <span class="default">not</span>
<span class="default">used</span> <span class="default">if</span> <span class="default">x</span> <span class="default">is</span> <span class="default">a</span> <span class="default">matrix</span>
<span class="default">freqrange</span><span class="default"> - </span><span class="default">string</span>
<span class="default">The</span> <span class="default">range</span> <span class="default">of</span> <span class="default">frequencies</span> <span class="default">over</span> <span class="default">which</span> <span class="default">the</span> <span class="default">pseudospetrogram</span> <span class="default">is</span>
<span class="default">computed</span><span class="default">. </span><span class="default">Three</span> <span class="default">possible</span> <span class="default">values</span><span class="default"> - </span>'<span class="default">onesided</span>'<span class="default">, </span>'<span class="default">twosided</span>'<span class="default">, </span>'<span class="default">centered</span>'
'<span class="default">corr</span>' <span class="default">flag</span>
<span class="default">Presence</span> <span class="default">indicates</span> <span class="default">that</span> <span class="default">the</span> <span class="default">primary</span> <span class="default">input</span> <span class="default">x</span> <span class="default">is</span> <span class="default">actually</span> <span class="default">a</span>
<span class="default">correlation</span> <span class="default">matrix</span>
<span class="default">Examples</span><span class="default">:</span>
<span class="default">TODO</span><span class="default">:</span></pre></div></div>
<div class="refsection"><h3 class="title">See also</h3>
<ul class="itemizedlist"><li class="member"><a href="rooteig.html" class="link">| pmusic | pmtm | pcov | pmcov | pburg | pyulear | pwelch | corrmtx</a></li></ul></div>
<div class="refsection"><h3 class="title">Authors</h3>
<ul class="itemizedlist"><li class="member">Ayush Baid</li>
<li class="member">References</li>
<li class="member">[1] Petre Stoica and Randolph Moses, Introduction To Spectral</li>
<li class="member">Analysis, Prentice-Hall, 1997, pg. 15</li>
<li class="member">[2] S. J. Orfanidis, Optimum Signal Processing. An Introduction.</li>
<li class="member">2nd Ed., Macmillan, 1988.</li></ul></div>
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