/usr/share/octave/packages/signal-1.3.0/invfreqs.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 88 89 90 91 92 93 94 | ## 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] = invfreqs(H,F,nB,nA)
## [B,A] = invfreqs(H,F,nB,nA,W)
## [B,A] = invfreqs(H,F,nB,nA,W,iter,tol,'trace')
##
## Fit filter B(s)/A(s)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: frequency (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 = [1/2 1];
## A = [1 1];
## w = linspace(0,4,128);
## H = freqs(B,A,w);
## [Bh,Ah] = invfreqs(H,w,1,1);
## Hh = freqs(Bh,Ah,w);
## plot(w,[abs(H);abs(Hh)])
## legend('Original','Measured');
## err = norm(H-Hh);
## disp(sprintf('L2 norm of frequency response error = %f',err));
## FIXME: check invfreq.m for todo's
function [B, A, SigN] = invfreqs(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, 's', varargin{:});
endfunction
%!demo
%! B = [1/2 1];
%! B = [1 0 0];
%! A = [1 1];
%! ##A = [1 36 630 6930 51975 270270 945945 2027025 2027025]/2027025;
%! A = [1 21 210 1260 4725 10395 10395]/10395;
%! A = [1 6 15 15]/15;
%! w = linspace(0, 8, 128);
%! H0 = freqs(B, A, w);
%! Nn = (randn(size(w))+j*randn(size(w)))/sqrt(2);
%! order = length(A) - 1;
%! [Bh, Ah, Sig0] = invfreqs(H0, w, [length(B)-1 2], length(A)-1);
%! Hh = freqs(Bh,Ah,w);
%! [BLS, ALS, SigLS] = invfreqs(H0+1e-5*Nn, w, [2 2], order, [], [], [], [], "method", "LS");
%! HLS = freqs(BLS, ALS, w);
%! [BTLS, ATLS, SigTLS] = invfreqs(H0+1e-5*Nn, w, [2 2], order, [], [], [], [], "method", "TLS");
%! HTLS = freqs(BTLS, ATLS, w);
%! [BMLS, AMLS, SigMLS] = invfreqs(H0+1e-5*Nn, w, [2 2], order, [], [], [], [], "method", "QR");
%! HMLS = freqs(BMLS, AMLS, w);
%! plot(w,[abs(H0); abs(Hh)])
%! xlabel("Frequency (rad/sec)");
%! ylabel("Magnitude");
%! legend('Original','Measured');
%! err = norm(H0-Hh);
%! disp(sprintf('L2 norm of frequency response error = %f',err));
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