Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/signal-1.1.3/invfreqz.m b/octave_packages/signal-1.1.3/invfreqz.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] = 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)));
+
+%% TODO: 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));
+            end
+        end
+    end
+  end
+end
+
+
+% 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);
+%! xlabel("Frequency (rad/sample)");
+%! 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));