--- /dev/null
+## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
+## Copyright (C) 2003 Doug Stewart <dastew@sympatico.ca>
+##
+## 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/>.
+
+## Generate an Chebyshev type II filter with Rs dB of stop band attenuation.
+##
+## [b, a] = cheby2(n, Rs, Wc)
+## low pass filter with cutoff pi*Wc radians
+##
+## [b, a] = cheby2(n, Rs, Wc, 'high')
+## high pass filter with cutoff pi*Wc radians
+##
+## [b, a] = cheby2(n, Rs, [Wl, Wh])
+## band pass filter with edges pi*Wl and pi*Wh radians
+##
+## [b, a] = cheby2(n, Rs, [Wl, Wh], 'stop')
+## band reject filter with edges pi*Wl and pi*Wh radians
+##
+## [z, p, g] = cheby2(...)
+## return filter as zero-pole-gain rather than coefficients of the
+## numerator and denominator polynomials.
+##
+## [...] = cheby2(...,'s')
+## return a Laplace space filter, W can be larger than 1.
+##
+## [a,b,c,d] = cheby2(...)
+## return state-space matrices
+##
+## References:
+##
+## Parks & Burrus (1987). Digital Filter Design. New York:
+## John Wiley & Sons, Inc.
+
+function [a,b,c,d] = cheby2(n, Rs, W, varargin)
+
+ if (nargin>5 || nargin<3) || (nargout>4 || nargout<2)
+ print_usage;
+ end
+
+ ## interpret the input parameters
+ if (!(length(n)==1 && n == round(n) && n > 0))
+ error ("cheby2: filter order n must be a positive integer");
+ end
+
+
+ stop = 0;
+ digital = 1;
+ for i=1:length(varargin)
+ switch varargin{i}
+ case 's', digital = 0;
+ case 'z', digital = 1;
+ case { 'high', 'stop' }, stop = 1;
+ case { 'low', 'pass' }, stop = 0;
+ otherwise, error ("cheby2: expected [high|stop] or [s|z]");
+ endswitch
+ endfor
+
+ [r, c]=size(W);
+ if (!(length(W)<=2 && (r==1 || c==1)))
+ error ("cheby2: frequency must be given as w0 or [w0, w1]");
+ elseif (!(length(W)==1 || length(W) == 2))
+ error ("cheby2: only one filter band allowed");
+ elseif (length(W)==2 && !(W(1) < W(2)))
+ error ("cheby2: first band edge must be smaller than second");
+ endif
+
+ if ( digital && !all(W >= 0 & W <= 1))
+ error ("cheby2: critical frequencies must be in (0 1)");
+ elseif ( !digital && !all(W >= 0 ))
+ error ("cheby2: critical frequencies must be in (0 inf)");
+ endif
+
+ if (Rs < 0)
+ error("cheby2: stopband attenuation must be positive decibels");
+ end
+
+ ## Prewarp to the band edges to s plane
+ if digital
+ T = 2; # sampling frequency of 2 Hz
+ W = 2/T*tan(pi*W/T);
+ endif
+
+ ## Generate splane poles and zeros for the chebyshev type 2 filter
+ ## From: Stearns, SD; David, RA; (1988). Signal Processing Algorithms.
+ ## New Jersey: Prentice-Hall.
+ C = 1; # default cutoff frequency
+ lambda = 10^(Rs/20);
+ phi = log(lambda + sqrt(lambda^2-1))/n;
+ theta = pi*([1:n]-0.5)/n;
+ alpha = -sinh(phi)*sin(theta);
+ beta = cosh(phi)*cos(theta);
+ if (rem(n,2))
+ ## drop theta==pi/2 since it results in a zero at infinity
+ zero = 1i*C./cos(theta([1:(n-1)/2, (n+3)/2:n]));
+ else
+ zero = 1i*C./cos(theta);
+ endif
+ pole = C./(alpha.^2+beta.^2).*(alpha-1i*beta);
+
+ ## Compensate for amplitude at s=0
+ ## Because of the vagaries of floating point computations, the
+ ## prod(pole)/prod(zero) sometimes comes out as negative and
+ ## with a small imaginary component even though analytically
+ ## the gain will always be positive, hence the abs(real(...))
+ gain = abs(real(prod(pole)/prod(zero)));
+
+ ## splane frequency transform
+ [zero, pole, gain] = sftrans(zero, pole, gain, W, stop);
+
+ ## Use bilinear transform to convert poles to the z plane
+ if digital
+ [zero, pole, gain] = bilinear(zero, pole, gain, T);
+ endif
+
+ ## convert to the correct output form
+ if nargout==2,
+ a = real(gain*poly(zero));
+ b = real(poly(pole));
+ elseif nargout==3,
+ a = zero;
+ b = pole;
+ c = gain;
+ else
+ ## output ss results
+ [a, b, c, d] = zp2ss (zero, pole, gain);
+ endif
+
+endfunction