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[CreaPhase.git] / octave_packages / signal-1.1.3 / cheby2.m

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+## 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