Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / signal-1.1.3 / cheby1.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 I filter with Rp dB of pass band ripple.
+## 
+## [b, a] = cheby1(n, Rp, Wc)
+##    low pass filter with cutoff pi*Wc radians
+##
+## [b, a] = cheby1(n, Rp, Wc, 'high')
+##    high pass filter with cutoff pi*Wc radians
+##
+## [b, a] = cheby1(n, Rp, [Wl, Wh])
+##    band pass filter with edges pi*Wl and pi*Wh radians
+##
+## [b, a] = cheby1(n, Rp, [Wl, Wh], 'stop')
+##    band reject filter with edges pi*Wl and pi*Wh radians
+##
+## [z, p, g] = cheby1(...)
+##    return filter as zero-pole-gain rather than coefficients of the
+##    numerator and denominator polynomials.
+##
+## [...] = cheby1(...,'s')
+##     return a Laplace space filter, W can be larger than 1.
+## 
+## [a,b,c,d] = cheby1(...)
+##  return  state-space matrices 
+## 
+## References: 
+##
+## Parks & Burrus (1987). Digital Filter Design. New York:
+## John Wiley & Sons, Inc.
+
+function [a,b,c,d] = cheby1(n, Rp, W, varargin)
+
+  if (nargin>5 || nargin<3) || (nargout>4 || nargout<2)
+    print_usage;
+  endif
+
+  ## interpret the input parameters
+  if (!(length(n)==1 && n == round(n) && n > 0))
+    error ("cheby1: filter order n must be a positive integer");
+  endif
+
+  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 ("cheby1: expected [high|stop] or [s|z]");
+    endswitch
+  endfor
+
+  [r, c]=size(W);
+  if (!(length(W)<=2 && (r==1 || c==1)))
+    error ("cheby1: frequency must be given as w0 or [w0, w1]");
+  elseif (!(length(W)==1 || length(W) == 2))
+    error ("cheby1: only one filter band allowed");
+  elseif (length(W)==2 && !(W(1) < W(2)))
+    error ("cheby1: first band edge must be smaller than second");
+  endif
+
+  if ( digital && !all(W >= 0 & W <= 1))
+    error ("cheby1: critical frequencies must be in (0 1)");
+  elseif ( !digital && !all(W >= 0 ))
+    error ("cheby1: critical frequencies must be in (0 inf)");
+  endif
+
+  if (Rp < 0)
+    error("cheby1: passband ripple 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 1 filter
+  C = 1; # default cutoff frequency
+  epsilon = sqrt(10^(Rp/10) - 1);
+  v0 = asinh(1/epsilon)/n;
+  pole = exp(1i*pi*[-(n-1):2:(n-1)]/(2*n));
+  pole = -sinh(v0)*real(pole) + 1i*cosh(v0)*imag(pole);
+  zero = [];
+
+  ## compensate for amplitude at s=0
+  gain = prod(-pole);
+  ## if n is even, the ripple starts low, but if n is odd the ripple
+  ## starts high. We must adjust the s=0 amplitude to compensate.
+  if (rem(n,2)==0)
+    gain = gain/10^(Rp/20);
+  endif
+
+  ## 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