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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from pmusic.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="pmusic" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
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xmlns:ns3="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>pmusic</refname>
<refpurpose>Computes Psuedospectrum using MUSIC algorithm</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
[S,w] = pmusic(x,p)
[S,w] = pmusic(x,p,w)
[S,w] = pmusic(x,p,nfft)
[S,w] = pmusic(x,p,nfft,fs)
[S,w] = pmusic(x,p,f,fs)
[S,f] = pmusic(...,'corr')
[S,f] = pmusic(x,p,nfft,fs,nwin,noverlap)
[...] = pmusic(...,freqrange)
[...,v,e] = pmusic(...)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>x:</term>
<listitem><para> int|double - vector|matrix</para>
<para>Input signal. In case of a matrix, each row of x represents a
seperate observation of the signal. If 'corr' flag is specified,
then x is the correlation matrix.
If w is not specified in the input, it is determined by the
algorithm. If x is real valued, then range of w is [0, pi].
Otherwise, the range of w is [0, 2pi)</para>
</listitem></varlistentry>
</variablelist>
<variablelist>
<varlistentry><term>p:</term>
<listitem><para> int|double - scalar|vector</para>
<para>p(1) is the dimension of the signal subspace
p(2), if specified, represents a threshold that is multiplied by
the smallest estimated eigenvalue of the signal's correlation matrix.</para>
</listitem></varlistentry>
</variablelist>
<variablelist>
<varlistentry><term>w:</term>
<listitem><para> int|double - vector</para>
<para>w is the vector of normalized frequencies over which the
pseuspectrogram is to be computed.</para>
</listitem></varlistentry>
</variablelist>
<variablelist>
<varlistentry><term>nfft:</term>
<listitem><para> int - scalar (Default = 256)</para>
<para>Length of the fft used to compute pseudospectrum. The length of S
(and hence w/f) depends on the type of values in x and nfft.
If x is real, length of s is (nfft/2 + 1) {Range of w = [0, pi]} if
nfft is even and (nfft+1)/2 {Range of w = [0, pi)} otherwise.
If x is complex, length of s is nfft.</para>
</listitem></varlistentry>
</variablelist>
<variablelist>
<varlistentry><term>fs:</term>
<listitem><para> int|double - scalar (Default = 1)</para>
<para>Sampling rate. Used to convert the normalized frequencies (w) to
actual values (f) and vice-versa.</para>
</listitem></varlistentry>
</variablelist>
<variablelist>
<varlistentry><term>nwin:</term>
<listitem><para> int|double - scalar (int only)|vector (Default = 2*p(1))</para>
<para> If nwin is scalar, it is the length of the rectangular window.
Otherwise, the vector input is considered as the window coefficients.
Not used if 'corr' flag present.</para>
</listitem></varlistentry>
</variablelist>
<variablelist>
<varlistentry><term>noverlap:</term>
<listitem><para> int - scalar (Default = nwin-1)</para>
<para> number of points by which successive windows overlap. noverlap not
used if x is a matrix</para>
</listitem></varlistentry>
</variablelist>
<variablelist>
<varlistentry><term>freqrange:</term>
<listitem><para> string</para>
<para>The range of frequencies over which the pseudospetrogram is
computed. Three possible values - 'onesided', 'twosided', 'centered'
'corr' flag
Presence indicates that the primary input x is actually a
correlation matrix
</para>
</listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>[S,w] = pmusic(x,p) implements the MUSIC (Multiple Signal Classification) algorithm and returns S, the pseudospectrum estimate of the input signal x, and a vector w of normalized frequencies (in rad/sample) at which the pseudospectrum is evaluated. The pseudospectrum is calculated using estimates of the eigenvectors of a correlation matrix associated with the input data x, where x is specified as either:</para>
<para> A row or column vector representing one observation of the signal
</para>
<para>A rectangular array for which each row of x represents a separate observation of the signal (for example, each row is one output of an array of sensors, as in array processing), such that x'*x is an estimate of the correlation matrix</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
n = 0:199;
x = cos(0.257*%pi*n) + sin(0.2*%pi*n) ;
[S,w]=pmusic(x,2,16,1)
]]></programlisting>
</refsection>
<refsection>
<title>See also</title>
<simplelist type="inline">
<member><link linkend="pburg">pburg| peig | periodogram | pmtm | prony | pwelch | rooteig | rootmusic</link></member>
</simplelist>
</refsection>
<refsection>
<title>Authors</title>
<simplelist type="vert">
<member>Ayush Baid</member>
<member>References</member>
<member>[1] Petre Stoica and Randolph Moses, Introduction To Spectral</member>
<member>Analysis, Prentice-Hall, 1997, pg. 15</member>
<member>[2] S. J. Orfanidis, Optimum Signal Processing. An Introduction.</member>
<member>2nd Ed., Macmillan, 1988.</member>
</simplelist>
</refsection>
</refentry>
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