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<TITLE>GNU Octave - Signal Processing</TITLE>
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<P><HR><P>
<H1><A NAME="SEC162" HREF="octave_toc.html#TOC162">Signal Processing</A></H1>
<P>
I hope that someday Octave will include more signal processing
functions. If you would like to help improve Octave in this area,
please contact @email{bug-octave@bevo.che.wisc.edu}.
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>detrend</B> <I>(<VAR>x</VAR>, <VAR>p</VAR>)</I>
<DD><A NAME="IDX803"></A>
If <VAR>x</VAR> is a vector, <CODE>detrend (<VAR>x</VAR>, <VAR>p</VAR>)</CODE> removes the
best fit of a polynomial of order <VAR>p</VAR> from the data <VAR>x</VAR>.
</P>
<P>
If <VAR>x</VAR> is a matrix, <CODE>detrend (<VAR>x</VAR>, <VAR>p</VAR>)</CODE> does the same
for each column in <VAR>x</VAR>.
</P>
<P>
The second argument is optional. If it is not specified, a value of 1
is assumed. This corresponds to removing a linear trend.
</DL>
</P>
<P>
<DL>
<DT><U>Function:</U> <B>fft</B> <I>(<VAR>a</VAR>, <VAR>n</VAR>)</I>
<DD><A NAME="IDX804"></A>
Compute the FFT of <VAR>a</VAR> using subroutines from FFTPACK. If <VAR>a</VAR>
is a matrix, <CODE>fft</CODE> computes the FFT for each column of <VAR>a</VAR>.
</P>
<P>
If called with two arguments, <VAR>n</VAR> is expected to be an integer
specifying the number of elements of <VAR>a</VAR> to use. If <VAR>a</VAR> is a
matrix, <VAR>n</VAR> specifies the number of rows of <VAR>a</VAR> to use. If
<VAR>n</VAR> is larger than the size of <VAR>a</VAR>, <VAR>a</VAR> is resized and
padded with zeros.
</DL>
</P>
<P>
<DL>
<DT><U>Loadable Function:</U> <B>ifft</B> <I>(<VAR>a</VAR>, <VAR>n</VAR>)</I>
<DD><A NAME="IDX805"></A>
Compute the inverse FFT of <VAR>a</VAR> using subroutines from FFTPACK. If
<VAR>a</VAR> is a matrix, <CODE>fft</CODE> computes the inverse FFT for each column
of <VAR>a</VAR>.
</P>
<P>
If called with two arguments, <VAR>n</VAR> is expected to be an integer
specifying the number of elements of <VAR>a</VAR> to use. If <VAR>a</VAR> is a
matrix, <VAR>n</VAR> specifies the number of rows of <VAR>a</VAR> to use. If
<VAR>n</VAR> is larger than the size of <VAR>a</VAR>, <VAR>a</VAR> is resized and
padded with zeros.
</DL>
</P>
<P>
<DL>
<DT><U>Loadable Function:</U> <B>fft2</B> <I>(<VAR>a</VAR>, <VAR>n</VAR>, <VAR>m</VAR>)</I>
<DD><A NAME="IDX806"></A>
Compute the two dimensional FFT of <VAR>a</VAR>.
</P>
<P>
The optional arguments <VAR>n</VAR> and <VAR>m</VAR> may be used specify the
number of rows and columns of <VAR>a</VAR> to use. If either of these is
larger than the size of <VAR>a</VAR>, <VAR>a</VAR> is resized and padded with
zeros.
</DL>
</P>
<P>
<DL>
<DT><U>Loadable Function:</U> <B>ifft2</B> <I>(<VAR>a</VAR>, <VAR>n</VAR>, <VAR>m</VAR>)</I>
<DD><A NAME="IDX807"></A>
Compute the two dimensional inverse FFT of <VAR>a</VAR>.
</P>
<P>
The optional arguments <VAR>n</VAR> and <VAR>m</VAR> may be used specify the
number of rows and columns of <VAR>a</VAR> to use. If either of these is
larger than the size of <VAR>a</VAR>, <VAR>a</VAR> is resized and padded with
zeros.
</DL>
</P>
<P>
<DL>
<DT><U>Built-in Function:</U> <B>fftconv</B> <I>(<VAR>a</VAR>, <VAR>b</VAR>, <VAR>n</VAR>)</I>
<DD><A NAME="IDX808"></A>
Return the convolution of the vectors <VAR>a</VAR> and <VAR>b</VAR>, as a vector
with length equal to the <CODE>length (a) + length (b) - 1</CODE>. If <VAR>a</VAR>
and <VAR>b</VAR> are the coefficient vectors of two polynomials, the returned
value is the coefficient vector of the product polynomial.
</P>
<P>
The computation uses the FFT by calling the function <CODE>fftfilt</CODE>. If
the optional argument <VAR>n</VAR> is specified, an N-point FFT is used.
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>fftfilt</B> <I>(<VAR>b</VAR>, <VAR>x</VAR>, <VAR>n</VAR>)</I>
<DD><A NAME="IDX809"></A>
</P>
<P>
With two arguments, <CODE>fftfilt</CODE> filters <VAR>x</VAR> with the FIR filter
<VAR>b</VAR> using the FFT.
</P>
<P>
Given the optional third argument, <VAR>n</VAR>, <CODE>fftfilt</CODE> uses the
overlap-add method to filter <VAR>x</VAR> with <VAR>b</VAR> using an N-point FFT.
</DL>
</P>
<P>
<DL>
<DT><U>Loadable Function:</U> y = <B>filter</B> <I>(<VAR>b</VAR>, <VAR>a</VAR>, <VAR>x</VAR>)</I>
<DD><A NAME="IDX810"></A>
Return the solution to the following linear, time-invariant difference
equation:
</P>
<PRE>
N M
SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x)
k=0 k=0
</PRE>
<P>
where
N=length(a)-1 and M=length(b)-1.
An equivalent form of this equation is:
</P>
<PRE>
N M
y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x)
k=1 k=0
</PRE>
<P>
where
c = a/a(1) and d = b/a(1).
</P>
<P>
In terms of the z-transform, y is the result of passing the discrete-
time signal x through a system characterized by the following rational
system function:
</P>
<PRE>
M
SUM d(k+1) z^(-k)
k=0
H(z) = ----------------------
N
1 + SUM c(k+1) z(-k)
k=1
</PRE>
</DL>
<P>
<DL>
<DT><U>Loadable Function:</U> [<VAR>y</VAR>, <VAR>sf</VAR>] = <B>filter</B> <I>(<VAR>b</VAR>, <VAR>a</VAR>, <VAR>x</VAR>, <VAR>si</VAR>)</I>
<DD><A NAME="IDX811"></A>
This is the same as the <CODE>filter</CODE> function described above, except
that <VAR>si</VAR> is taken as the initial state of the system and the final
state is returned as <VAR>sf</VAR>. The state vector is a column vector
whose length is equal to the length of the longest coefficient vector
minus one. If <VAR>si</VAR> is not set, the initial state vector is set to
all zeros.
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> [<VAR>h</VAR>, <VAR>w</VAR>] = <B>freqz</B> <I>(<VAR>b</VAR>, <VAR>a</VAR>, <VAR>n</VAR>, "whole")</I>
<DD><A NAME="IDX812"></A>
Return the complex frequency response <VAR>h</VAR> of the rational IIR filter
whose numerator and denominator coefficients are <VAR>b</VAR> and <VAR>a</VAR>,
respectively. The response is evaluated at <VAR>n</VAR> angular frequencies
between 0 and
2*pi.
</P>
<P>
The output value <VAR>w</VAR> is a vector of the frequencies.
</P>
<P>
If the fourth argument is omitted, the response is evaluated at
frequencies between 0 and
pi.
</P>
<P>
If <VAR>n</VAR> is omitted, a value of 512 is assumed.
</P>
<P>
If <VAR>a</VAR> is omitted, the denominator is assumed to be 1 (this
corresponds to a simple FIR filter).
</P>
<P>
For fastest computation, <VAR>n</VAR> should factor into a small number of
small primes.
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>sinc</B> <I>(<VAR>x</VAR>)</I>
<DD><A NAME="IDX813"></A>
Return
sin(pi*x)/(pi*x).
</DL>
</P>
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