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butter.m

## Copyright (C) 1999 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

## Generate a butterworth filter.
## 
## [b,a] = butter(n, Wc)
##    low pass filter with cutoff pi*Wc radians
##
## [b,a] = butter(n, Wc, 'high')
##    high pass filter with cutoff pi*Wc radians
##
## [b,a] = butter(n, [Wl, Wh])
##    band pass filter with edges pi*Wl and pi*Wh radians
##
## [b,a] = butter(n, [Wl, Wh], 'stop')
##    band reject filter with edges pi*Wl and pi*Wh radians
##
## [z,p,g] = butter(...)
##    return filter as zero-pole-gain rather than coefficients of the
##    numerator and denominator polynomials.
## 
## References: 
##
## Proakis & Manolakis (1992). Digital Signal Processing. New York:
## Macmillan Publishing Company.

## Author: pkienzle@cs.indiana.edu

function [Zz, Zp, Zg] = butter(n, W, stype)

  if (nargin>3 || nargin<2) || (nargout>3 || nargout<2)
    usage ("[b, a] or [z, p, g] = butter (n, W, [, 'ftype'])");
  end

  ## interpret the input parameters
  if (!(length(n)==1 && n == round(n) && n > 0))
    error ("butter: filter order n must be a positive integer");
  end

  stop = nargin==3;
  if stop && !(strcmp(stype, 'high') || strcmp(stype, 'stop'))
    error ("butter: ftype must be 'high' or 'stop'");
  end

  [r, c]=size(W);
  if (!(length(W)<=2 && (r==1 || c==1)))
    error ("butter: frequency must be given as w0 or [w0, w1]");
  elseif (!all(W >= 0 & W <= 1))
    error ("butter: critical frequencies must be in (0 1)");
  elseif (!(length(W)==1 || length(W) == 2))
    error ("butter: only one filter band allowed");
  elseif (length(W)==2 && !(W(1) < W(2)))
    error ("butter: first band edge must be smaller than second");
  endif

  ## Prewarp to the band edges to s plane
  T = 2;       # sampling frequency of 2 Hz
  Ws = 2/T*tan(pi*W/T);

  ## Generate splane poles for the prototype butterworth filter
  ## source: Kuc
  C = 1; # default cutoff frequency
  Sp = C*exp(1i*pi*(2*[1:n] + n - 1)/(2*n));
  Sz = ;
  Sg = C^n;

  ## splane frequency transform
  [Sz, Sp, Sg] = sftrans(Sz, Sp, Sg, Ws, stop);

  ## Use bilinear transform to convert poles to the z plane
  [Zz, Zp, Zg] = bilinear(Sz, Sp, Sg, T);

  if nargout==2, [Zz, Zp] = zp2tf(Zz, Zp, Zg); endif

endfunction

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