## 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; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {[B,A] =} invfreqs(H,F,nB,nA)
## @deftypefnx {} {[B,A] =} invfreqs(H,F,nB,nA,W)
## @deftypefnx {} {[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:
## @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));
## @end example
## @end deftypefn

## 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));
