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}.
detrend (x, p)
removes the
best fit of a polynomial of order p from the data x.
If x is a matrix, detrend (x, p)
does the same
for each column in x.
The second argument is optional. If it is not specified, a value of 1 is assumed. This corresponds to removing a linear trend.
fft
computes the FFT for each column of a.
If called with two arguments, n is expected to be an integer specifying the number of elements of a to use. If a is a matrix, n specifies the number of rows of a to use. If n is larger than the size of a, a is resized and padded with zeros.
fft
computes the inverse FFT for each column
of a.
If called with two arguments, n is expected to be an integer specifying the number of elements of a to use. If a is a matrix, n specifies the number of rows of a to use. If n is larger than the size of a, a is resized and padded with zeros.
The optional arguments n and m may be used specify the number of rows and columns of a to use. If either of these is larger than the size of a, a is resized and padded with zeros.
The optional arguments n and m may be used specify the number of rows and columns of a to use. If either of these is larger than the size of a, a is resized and padded with zeros.
length (a) + length (b) - 1
. If a
and b are the coefficient vectors of two polynomials, the returned
value is the coefficient vector of the product polynomial.
The computation uses the FFT by calling the function fftfilt
. If
the optional argument n is specified, an N-point FFT is used.
With two arguments, fftfilt
filters x with the FIR filter
b using the FFT.
Given the optional third argument, n, fftfilt
uses the
overlap-add method to filter x with b using an N-point FFT.
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
where N=length(a)-1 and M=length(b)-1. An equivalent form of this equation is:
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
where c = a/a(1) and d = b/a(1).
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:
M SUM d(k+1) z^(-k) k=0 H(z) = ---------------------- N 1 + SUM c(k+1) z(-k) k=1
filter
function described above, except
that si is taken as the initial state of the system and the final
state is returned as sf. The state vector is a column vector
whose length is equal to the length of the longest coefficient vector
minus one. If si is not set, the initial state vector is set to
all zeros.
The output value w is a vector of the frequencies.
If the fourth argument is omitted, the response is evaluated at frequencies between 0 and pi.
If n is omitted, a value of 512 is assumed.
If a is omitted, the denominator is assumed to be 1 (this corresponds to a simple FIR filter).
For fastest computation, n should factor into a small number of small primes.
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