Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/signal-1.1.3/buttord.m b/octave_packages/signal-1.1.3/buttord.m
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+## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
+##
+## 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/>.
+
+## Compute butterworth 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] = buttord(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] = buttord([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.
+##
+## Theory: |H(W)|^2 = 1/[1+(W/Wc)^(2N)] = 10^(-R/10)
+## With some algebra, you can solve simultaneously for Wc and N given
+## Ws,Rs and Wp,Rp.  For high pass filters, subtracting the band edges
+## from Fs/2, performing the test, and swapping the resulting Wc back
+## works beautifully.  For bandpass and bandstop filters this process
+## significantly overdesigns.  Artificially dividing N by 2 in this case
+## helps a lot, but it still overdesigns.
+##
+## See also: butter
+
+function [n, Wc] = buttord(Wp, Ws, Rp, Rs)
+  if nargin != 4
+    print_usage;
+  elseif length(Wp) != length(Ws)
+    error("buttord: Wp and Ws must have the same length");
+  elseif length(Wp) != 1 && length(Wp) != 2
+    error("buttord: 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("buttord: Wp(1)<Ws(1)<Ws(2)<Wp(2) or Ws(1)<Wp(1)<Wp(2)<Ws(2)");
+  end
+
+  if length(Wp) == 2
+    warning("buttord: seems to overdesign bandpass and bandreject filters");
+  end
+
+  T = 2;
+  
+  ## if high pass, reverse the sense of the test
+  stop = find(Wp > Ws);
+  Wp(stop) = 1-Wp(stop); # stop will be at most length 1, so no need to
+  Ws(stop) = 1-Ws(stop); # subtract from ones(1,length(stop))
+  
+  ## warp the target frequencies according to the bilinear transform
+  Ws = (2/T)*tan(pi*Ws./T);
+  Wp = (2/T)*tan(pi*Wp./T);
+  
+  ## compute minimum n which satisfies all band edge conditions
+  ## the factor 1/length(Wp) is an artificial correction for the
+  ## band pass/stop case, which otherwise significantly overdesigns.
+  qs = log(10^(Rs/10) - 1);
+  qp = log(10^(Rp/10) - 1);
+  n = ceil(max(0.5*(qs - qp)./log(Ws./Wp))/length(Wp));
+
+  ## compute -3dB cutoff given Wp, Rp and n
+  Wc = exp(log(Wp) - qp/2/n);
+
+  ## unwarp the returned frequency
+  Wc = atan(T/2*Wc)*T/pi;
+  
+  ## if high pass, reverse the sense of the test
+  Wc(stop) = 1-Wc(stop);
+    
+endfunction