Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / signal-1.1.3 / invfreqs.m

diff --git a/octave_packages/signal-1.1.3/invfreqs.m b/octave_packages/signal-1.1.3/invfreqs.m
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+%% 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));
+
+% TODO: 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));
+              end
+          end
+      end
+    end
+  end
+
+  % 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);
+%! xlabel("Frequency (rad/sec)");
+%! ylabel("Magnitude");
+%! plot(w,[abs(H0); abs(Hh)])
+%! legend('Original','Measured');
+%! err = norm(H0-Hh);
+%! disp(sprintf('L2 norm of frequency response error = %f',err));