/tags/cvs_final/octave-forge/main/signal/inst/cheb1ord.m

## Copyright (C) 2000 Paul Kienzle
##
## 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 2 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, write to the Free Software
## Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
##
## Completed by: Laurent S. Mazet

## Compute chebyshev type I filter order and cutoff for the desired response
## characteristics. Rp is the allowable decibels of ripple in the pass 
## band. Rs is the minimum attenuation in the stop band.
##
## [n, Wc] = cheb1ord(Wp, Ws, Rp, Rs)
##     Low pass (Wp<Ws) or high pass (Wp>Ws) filter design.  Wp is the
##     pass band edge and Ws is the stop band edge.  Frequencies are
##     normalized to [0,1], corresponding to the range [0,Fs/2].
## 
## [n, Wc] = cheb1ord([Wp1, Wp2], [Ws1, Ws2], Rp, Rs)
##     Band pass (Ws1<Wp1<Wp2<Ws2) or band reject (Wp1<Ws1<Ws2<Wp2)
##     filter design. Wp gives the edges of the pass band, and Ws gives
##     the edges of the stop band.
##
## See also: cheby1

function [n, Wc] = cheb1ord(Wp, Ws, Rp, Rs)

  if nargin != 4
    usage("[n, Wn] = cheb1ord(Wp, Ws, Rp, Rs)");
  elseif length(Wp) != length(Ws)
    error("cheb1ord: Wp and Ws must have the same length");
  elseif length(Wp) != 1 && length(Wp) != 2
    error("cheb1ord: Wp,Ws must have length 1 or 2");
  elseif length(Wp) == 2 && ...
	(all(Wp>Ws) || all(Ws>Wp) || diff(Wp)<=0 || diff(Ws)<=0)
    error("cheb1ord: Wp(1)<Ws(1)<Ws(2)<Wp(2) or Ws(1)<Wp(1)<Wp(2)<Ws(2)");
  end

  T = 2;

  ## returned frequency is the same as the input frequency
  Wc = Wp;

  ## warp the target frequencies according to the bilinear transform
  Ws = (2/T)*tan(pi*Ws./T);
  Wp = (2/T)*tan(pi*Wp./T);

  if (Wp(1) < Ws(1))
    ## low pass
    if (length(Wp) == 1)
      Wa = Ws/Wp;
    else
      ## band reject
      error ("band reject is not implement yet.");
    endif;
  else
   ## if high pass, reverse the sense of the test
   if (length(Wp) == 1)
      Wa = Wp/Ws;
    else
      ## band pass 
      Wa=(Ws.^2 - Wp(1)*Wp(2))./(Ws*(Wp(1)-Wp(2)));
    endif;
  endif;
  Wa = min(abs(Wa));
  
  ## compute minimum n which satisfies all band edge conditions
  stop_atten = 10^(abs(Rs)/10);
  pass_atten = 10^(abs(Rp)/10);
  n = ceil(acosh(sqrt((stop_atten-1)/(pass_atten-1)))/acosh(Wa));

endfunction

%!demo
%! Fs = 10000; 
%! [n, Wc] = cheb1ord (1000/(Fs/2), 1200/(Fs/2), 0.5, 29);
%!
%! subplot (221);
%! axis ([ 0, 1500, -1, 0]);
%! title("Pass band Wp=1000 Rp=0.5");
%! xlabel("Frequency (Hz)");
%! ylabel("Attenuation (dB)");
%! grid;
%! plot ([0, 1000, 1000, 0, 0], [0, 0, -0.5, -0.5, 0], ";;");
%! hold on;
%! [b, a] = cheby1 (n, 0.5, Wc);
%! [h, w] = freqz (b, a, [], Fs);
%! plot (w, 20*log10(abs(h)), ";;");
%! hold off;
%!
%! subplot (222);
%! axis ([ 0, Fs/2, -250, 0]);
%! title("Stop band Ws=1200 Rs=29");
%! xlabel("Frequency (Hz)");
%! ylabel("Attenuation (dB)");
%! grid;
%! plot ([1200, Fs/2, Fs/2, 1200, 1200], [-29, -29, -500, -500, -29], ";;");
%! hold on;
%! [b, a] = cheby1 (n, 0.5, Wc);
%! [h, w] = freqz (b, a, [], Fs);
%! plot (w, 20*log10(abs(h)), ";;");
%! hold off;
%!
%! subplot (223);
%! axis ([ 990, 1010, -0.6, -0.4]);
%! title("Pass band detail Wp=1000 Rp=0.5");
%! xlabel("Frequency (Hz)");
%! ylabel("Attenuation (dB)");
%! grid;
%! plot ([0, 1000, 1000, 0, 0], [0, 0, -0.5, -0.5, 0], ";;");
%! hold on;
%! [b, a] = cheby1 (n, 0.5, Wc);
%! [h, w] = freqz (b, a, [990:1010], Fs);
%! plot (w, 20*log10(abs(h)), ";filter n;");
%! [b, a] = cheby1 (n-1, 0.5, Wc);
%! [h, w] = freqz (b, a, [990:1010], Fs);
%! plot (w, 20*log10(abs(h)), ";filter n-1;");
%! [b, a] = cheby1 (n+1, 0.5, Wc);
%! [h, w] = freqz (b, a, [990:1010], Fs);
%! plot (w, 20*log10(abs(h)), ";filter n+1;");
%! hold off;
%!
%! subplot (224);
%! axis ([ 1190, 1210, -40, -20]);
%! title("Stop band detail Wp=1200 Rp=29");
%! xlabel("Frequency (Hz)");
%! ylabel("Attenuation (dB)");
%! grid;
%! plot ([1200, Fs/2, Fs/2, 1200, 1200], [-29, -29, -500, -500, -29], ";;");
%! hold on;
%! [b, a] = cheby1 (n, 0.5, Wc);
%! [h, w] = freqz (b, a, [1190:1210], Fs);
%! plot (w, 20*log10(abs(h)), ";filter n;");
%! [b, a] = cheby1 (n-1, 0.5, Wc);
%! [h, w] = freqz (b, a, [1190:1210], Fs);
%! plot (w, 20*log10(abs(h)), ";filter n-1;");
%! [b, a] = cheby1 (n+1, 0.5, Wc);
%! [h, w] = freqz (b, a, [1190:1210], Fs);
%! plot (w, 20*log10(abs(h)), ";filter n+1;");
%! hold off;