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########################################################################
##
## Copyright (C) 1994-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {[@var{h}, @var{w}] =} freqz (@var{b}, @var{a}, @var{n}, "whole")
## @deftypefnx {} {[@var{h}, @var{w}] =} freqz (@var{b})
## @deftypefnx {} {[@var{h}, @var{w}] =} freqz (@var{b}, @var{a})
## @deftypefnx {} {[@var{h}, @var{w}] =} freqz (@var{b}, @var{a}, @var{n})
## @deftypefnx {} {@var{h} =} freqz (@var{b}, @var{a}, @var{w})
## @deftypefnx {} {[@var{h}, @var{w}] =} freqz (@dots{}, @var{Fs})
## @deftypefnx {} {} freqz (@dots{})
##
## Return the complex frequency response @var{h} of the rational IIR filter
## whose numerator and denominator coefficients are @var{b} and @var{a},
## respectively.
##
## The response is evaluated at @var{n} angular frequencies between 0 and
## @ifnottex
## 2*pi.
## @end ifnottex
## @tex
## $2\pi$.
## @end tex
##
## @noindent
## The output value @var{w} is a vector of the frequencies.
##
## If @var{a} is omitted, the denominator is assumed to be 1 (this
## corresponds to a simple FIR filter).
##
## If @var{n} is omitted, a value of 512 is assumed. For fastest computation,
## @var{n} should factor into a small number of small primes.
##
## If the fourth argument, @qcode{"whole"}, is omitted the response is
## evaluated at frequencies between 0 and
## @ifnottex
## pi.
## @end ifnottex
## @tex
## $\pi$.
## @end tex
##
## @code{freqz (@var{b}, @var{a}, @var{w})}
##
## Evaluate the response at the specific frequencies in the vector @var{w}.
## The values for @var{w} are measured in radians.
##
## @code{[@dots{}] = freqz (@dots{}, @var{Fs})}
##
## Return frequencies in Hz instead of radians assuming a sampling rate
## @var{Fs}. If you are evaluating the response at specific frequencies
## @var{w}, those frequencies should be requested in Hz rather than radians.
##
## @code{freqz (@dots{})}
##
## Plot the magnitude and phase response of @var{h} rather than returning them.
##
## @seealso{freqz_plot}
## @end deftypefn
function [h_r, f_r] = freqz (b, a, n, region, Fs)
if (nargin < 1)
print_usage ();
elseif (nargin == 1)
## Response of an FIR filter.
a = n = region = Fs = [];
elseif (nargin == 2)
## Response of an IIR filter
n = region = Fs = [];
elseif (nargin == 3)
region = Fs = [];
elseif (nargin == 4)
Fs = [];
if (! ischar (region) && ! isempty (region))
Fs = region;
region = [];
endif
endif
if (isempty (b))
b = 1;
elseif (! isvector (b))
error ("freqz: B must be a vector");
endif
if (isempty (a))
a = 1;
elseif (! isvector (a))
error ("freqz: A must be a vector");
endif
if (isempty (n))
n = 512;
elseif (isscalar (n) && n < 1)
error ("freqz: N must be a positive integer");
endif
if (isempty (region))
if (isreal (b) && isreal (a))
region = "half";
else
region = "whole";
endif
endif
if (isempty (Fs))
freq_norm = true;
if (nargout == 0)
Fs = 2;
else
Fs = 2*pi;
endif
else
freq_norm = false;
endif
plot_output = (nargout == 0);
whole_region = strcmp (region, "whole");
a = a(:);
b = b(:);
if (! isscalar (n))
## Explicit frequency vector given
w = f = n;
if (nargin == 4)
## Sampling rate Fs was specified
w = 2*pi*f/Fs;
endif
k = max (length (b), length (a));
hb = polyval (postpad (b, k), exp (j*w));
ha = polyval (postpad (a, k), exp (j*w));
else
## polyval(fliplr(P),exp(jw)) is O(p n) and fft(x) is O(n log(n)),
## where p is the order of the polynomial P. For small p it
## would be faster to use polyval but in practice the overhead for
## polyval is much higher and the little bit of time saved isn't
## worth the extra code.
k = max (length (b), length (a));
if (k > n/2 && nargout == 0)
## Ensure a causal phase response.
n *= 2 .^ ceil (log2 (2*k/n));
endif
if (whole_region)
N = n;
if (plot_output)
f = Fs * (0:n).' / N; # do 1 more for the plot
else
f = Fs * (0:n-1).' / N;
endif
else
N = 2*n;
if (plot_output)
n += 1;
endif
f = Fs * (0:n-1).' / N;
endif
pad_sz = N*ceil (k/N);
b = postpad (b, pad_sz);
a = postpad (a, pad_sz);
hb = zeros (n, 1);
ha = zeros (n, 1);
for i = 1:N:pad_sz
hb += fft (postpad (b(i:i+N-1), N))(1:n);
ha += fft (postpad (a(i:i+N-1), N))(1:n);
endfor
endif
h = hb ./ ha;
if (plot_output)
## Plot and don't return values.
if (whole_region && isscalar (n))
h(end+1) = h(1); # Solution is periodic. Copy first value to end.
endif
freqz_plot (f, h, freq_norm);
else
## Return values and don't plot.
h_r = h;
f_r = f;
endif
endfunction
%!testif HAVE_FFTW # correct values and fft-polyval consistency
%! ## butterworth filter, order 2, cutoff pi/2 radians
%! b = [0.292893218813452 0.585786437626905 0.292893218813452];
%! a = [1 0 0.171572875253810];
%! [h,w] = freqz (b,a,32);
%! assert (h(1),1,10*eps);
%! assert (abs (h(17)).^2,0.5,10*eps);
%! assert (h,freqz (b,a,w),10*eps); # fft should be consistent with polyval
%!testif HAVE_FFTW # whole-half consistency
%! b = [1 1 1]/3; # 3-sample average
%! [h,w] = freqz (b,1,32,"whole");
%! assert (h(2:16),conj (h(32:-1:18)),20*eps);
%! [h2,w2] = freqz (b,1,16,"half");
%! assert (h(1:16),h2,20*eps);
%! assert (w(1:16),w2,20*eps);
%!testif HAVE_FFTW # Sampling frequency properly interpreted
%! b = [1 1 1]/3; a = [1 0.2];
%! [h,f] = freqz (b,a,16,320);
%! assert (f,[0:15]'*10,10*eps);
%! [h2,f2] = freqz (b,a,[0:15]*10,320);
%! assert (f2,[0:15]*10,10*eps);
%! assert (h,h2.',20*eps);
%! [h3,f3] = freqz (b,a,32,"whole",320);
%! assert (f3,[0:31]'*10,10*eps);
## Test input validation
## FIXME: Need to put tests here and simplify input validation in the main code.
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