It bothers me for quite some time that the signal processing toolbox
misses besself and besselap. So I gave a try at implementing them.
It would be nice if they could be added to octave-forge.
Thanks,
Tom
## Copyright (C) 2009 Thomas Sailer
##
## 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, see <http://www.gnu.org/licenses/>.
## Return bessel analog filter prototype.
##
## References:
##
## http://en.wikipedia.org/wiki/Bessel_polynomials
function [zero, pole, gain] = besselap (n)
if (nargin>1 || nargin<1)
usage ("[z, p, g] = besselap (n)");
end
## interpret the input parameters
if (!(length(n)==1 && n == round(n) && n > 0))
error ("besselap: filter order n must be a positive integer");
end
p0=1;
p1=[1 1];
for nn=2:n;
px=(2*nn-1)*p1;
py=[p0 0 0];
px=prepad(px,max(length(px),length(py)),0);
py=prepad(py,length(px));
p0=p1;
p1=px+py;
endfor;
% p1 now contains the reverse bessel polynomial for n
% scale it by replacing s->s/w0 so that the gain becomes 1
p1=p1.*p1(length(p1)).^((length(p1)-1:-1:0)/(length(p1)-1));
zero=[];
pole=roots(p1);
gain=1;
endfunction
## Copyright (C) 2009 Thomas Sailer
## 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, see <http://www.gnu.org/licenses/>.
## Generate a bessel filter.
## Default is a Laplace space (s) filter.
##
## [b,a] = besself(n, Wc)
## low pass filter with cutoff pi*Wc radians
##
## [b,a] = besself(n, Wc, 'high')
## high pass filter with cutoff pi*Wc radians
##
## [b,a] = besself(n, [Wl, Wh])
## band pass filter with edges pi*Wl and pi*Wh radians
##
## [b,a] = besself(n, [Wl, Wh], 'stop')
## band reject filter with edges pi*Wl and pi*Wh radians
##
## [z,p,g] = besself(...)
## return filter as zero-pole-gain rather than coefficients of the
## numerator and denominator polynomials.
##
## [...] = besself(...,'z')
## return a discrete space (Z) filter, W must be less than 1.
##
## [a,b,c,d] = besself(...)
## return state-space matrices
##
## References:
##
## Proakis & Manolakis (1992). Digital Signal Processing. New York:
## Macmillan Publishing Company.
## Author: Paul Kienzle <pkien...@user.sf.net>
## Modified by: Doug Stewart <das...@sympatico.ca> Feb, 2003
function [a, b, c, d] = besself (n, W, varargin)
if (nargin>4 || nargin<2) || (nargout>4 || nargout<2)
usage ("[b, a] or [z, p, g] or [a,b,c,d] = besself (n, W [, 'ftype'][,'z'])");
end
## interpret the input parameters
if (!(length(n)==1 && n == round(n) && n > 0))
error ("besself: filter order n must be a positive integer");
end
stop = 0;
digital = 0;
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 ("besself: expected [high|stop] or [s|z]");
endswitch
endfor
[r, c]=size(W);
if (!(length(W)<=2 && (r==1 || c==1)))
error ("besself: frequency must be given as w0 or [w0, w1]");
elseif (!(length(W)==1 || length(W) == 2))
error ("besself: only one filter band allowed");
elseif (length(W)==2 && !(W(1) < W(2)))
error ("besself: first band edge must be smaller than second");
endif
if ( digital && !all(W >= 0 & W <= 1))
error ("besself: critical frequencies must be in (0 1)");
elseif ( !digital && !all(W >= 0 ))
error ("besself: critical frequencies must be in (0 inf)");
endif
## 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 for the prototype bessel filter
[zero, pole, gain] = besselap(n);
## 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
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