1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
|
<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from rootmusic.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="rootmusic" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
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>rootmusic</refname>
<refpurpose>Frequencies and power of sinusoids using the root MUSIC algorithm</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
w = rootmusic(x,p)
[w,pow] = rootmusic(x,p)
[f,pow] = rootmusc(...,fs)
[w,pow] = rootmusic(...,'corr')
</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>pow:</term>
<listitem><para> the estimated absolute value squared amplitudes of the sinusoids at the frequencies w.</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>corr:</term>
<listitem><para> If specified, x is interpreted as a correlation matrix rather than a matrix of the signal data. For x to be a correlation matrix, x must be a square matrix and all its eigenvalues must be nonnegative.</para>
</listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>W = rootmusic(X,P) returns the frequencies in radians/sample for the P complex exponentials (sinusoids) that make up the signal X.
The input X is specified either as:</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=0:99;
s=exp(1*%i*%pi/2*n)+2*exp(1*%i*%pi/4*n)+exp(1*%i*%pi/3*n)+rand(1,100,"normal");
[A,R]=corrmtx(s,12,'mod');
[W,P] = rootmusic(R,3,'corr');
]]></programlisting>
</refsection>
<refsection>
<title>See also</title>
<simplelist type="inline">
<member><link linkend="corrmtx">| peig | pmusic | rooteig</link></member>
<member><link linkend="References">References</link></member>
<member><link linkend="1)">Monson H. Hayes, Statistical Digital Signal Processing And Modeling,</link></member>
<member><link linkend="Wiley">& Sons, Inc, [Section 8.6.3]</link></member>
<member><link linkend="Output">arguments</link></member>
<member><link linkend="w">- double - vector</link></member>
<member><link linkend="Estimated">frequencies of the complex sinusoids</link></member>
<member><link linkend="pow">- double - vector</link></member>
<member><link linkend="estimated">absolute value squared amplitudes of the sinusoids at</link></member>
<member><link linkend="the">frequencies w</link></member>
</simplelist>
</refsection>
</refentry>
|
