/usr/share/octave/packages/signal-1.3.0/invfreqz.m is in octave-signal 1.3.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | ## Copyright (C) 1986,2003 Julius O. Smith III <jos@ccrma.stanford.edu>
## Copyright (C) 2003 Andrew Fitting
##
## This program 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.
##
## This program 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
## this program; if not, see <http://www.gnu.org/licenses/>.
## usage: [B,A] = invfreqz(H,F,nB,nA)
## [B,A] = invfreqz(H,F,nB,nA,W)
## [B,A] = invfreqz(H,F,nB,nA,W,iter,tol,'trace')
##
## Fit filter B(z)/A(z)to the complex frequency response H at frequency
## points F. A and B are real polynomial coefficients of order nA and nB.
## Optionally, the fit-errors can be weighted vs frequency according to
## the weights W.
## Note: all the guts are in invfreq.m
##
## H: desired complex frequency response
## F: normalized frequncy (0 to pi) (must be same length as H)
## nA: order of the denominator polynomial A
## nB: order of the numerator polynomial B
## W: vector of weights (must be same length as F)
##
## Example:
## [B,A] = butter(4,1/4);
## [H,F] = freqz(B,A);
## [Bh,Ah] = invfreq(H,F,4,4);
## Hh = freqz(Bh,Ah);
## disp(sprintf('||frequency response error|| = %f',norm(H-Hh)));
## FIXME: check invfreq.m for todo's
function [B, A, SigN] = invfreqz(H, F, nB, nA, W, iter, tol, tr, varargin)
if nargin < 9
varargin = {};
if nargin < 8
tr = '';
if nargin < 7
tol = [];
if nargin < 6
iter = [];
if nargin < 5
W = ones(1,length(F));
endif
endif
endif
endif
endif
## now for the real work
[B, A, SigN] = invfreq(H, F, nB, nA, W, iter, tol, tr, 'z', varargin{:});
endfunction
%!demo
%! order = 9; # order of test filter
%! # going to 10 or above leads to numerical instabilities and large errors
%! fc = 1/2; # sampling rate / 4
%! n = 128; # frequency grid size
%! [B0, A0] = butter(order, fc);
%! [H0, w] = freqz(B0, A0, n);
%! Nn = (randn(size(w))+j*randn(size(w)))/sqrt(2);
%! [Bh, Ah, Sig0] = invfreqz(H0, w, order, order);
%! [Hh, wh] = freqz(Bh, Ah, n);
%! [BLS, ALS, SigLS] = invfreqz(H0+1e-5*Nn, w, order, order, [], [], [], [], "method", "LS");
%! HLS = freqz(BLS, ALS, n);
%! [BTLS, ATLS, SigTLS] = invfreqz(H0+1e-5*Nn, w, order, order, [], [], [], [], "method", "TLS");
%! HTLS = freqz(BTLS, ATLS, n);
%! [BMLS, AMLS, SigMLS] = invfreqz(H0+1e-5*Nn, w, order, order, [], [], [], [], "method", "QR");
%! HMLS = freqz(BMLS, AMLS, n);
%! plot(w,[abs(H0) abs(Hh)])
%! xlabel("Frequency (rad/sample)");
%! ylabel("Magnitude");
%! legend('Original','Measured');
%! err = norm(H0-Hh);
%! disp(sprintf('L2 norm of frequency response error = %f',err));
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