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// Copyright (C) 2018 - IIT Bombay - FOSSEE
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
// Original Source : https://octave.sourceforge.io/signal/
// Modifieded by:Sonu Sharma, RGIT Mumbai
// Organization: FOSSEE, IIT Bombay
// Email: toolbox@scilab.in
function [a, b, c, d] = besself (n, w, varargin)
//Bessel filter design.
//Canding Sequence
//[b, a] = besself(n, Wc)
//[b, a] = besself (n, Wc, "high")
//[b, a] = besself (n, [Wl, Wh])
//[b, a] = besself (n, [Wl, Wh], "stop")
//[z, p, g] = besself (…)
//[…] = besself (…, "z")
//Parameters
//n: positive integer value (order of filter)
//Wc: positive real value,
// 1).Analog 3dB cutoff frequency/frequencies for analog filter, in the range [0, Inf] {rad/sec}
// 2).Normalised digital 3dB cutoff frequency/frequencies for digital filter, in the range [0, 1] {dimensionless}
//Description
//This function generates a Bessel filter. The default is a Laplace space (s) or analog filter.
//If second argument is scalar the third parameter takes in high or low, the default value being low. The cutoff is Wc rad/sec.
//If second argument is vector of length 2 ie [Wl Wh] then third parameter may be pass or stop default is pass for bandpass and band reject filter respectively
//[z,p,g] = besself(...) returns filter as zero-pole-gain rather than coefficients of the numerator and denominator polynomials.
//[...] = besself(...,’z’) returns a discrete space (Z) filter. Wc must be less than 1 {dimensionless}.
//Examples
//[b, a]=besself(2,.3,"high","z")
//Output :
// a =
//
// 1. - 0.6912562 0.1760353
// b =
//
// 0.4668229 - 0.9336457 0.4668229
//
funcprot(0);
[nargout nargin] = argn();
if (nargin > 4 | nargin < 2 | nargout > 4 | nargout < 2)
error("besself: invalid number of inputs")
end
// interpret the input parameters
if (~ (isscalar (n) & (n == fix (n)) & (n > 0)))
error ("besself: filter order N must be a positive integer");
end
stop = %F;
digital = %F;
for i = 1:length (varargin)
select (varargin(i))
case "s"
digital = %F;
case "z"
digital = %T;
case "high"
stop = %T;
case "stop"
stop = %T;
case "low"
stop = %F;
case "pass"
stop = %F;
else
error ("besself: expected [high|stop] or [s|z]");
end
end
// FIXME: Band-pass and stop-band currently non-functional, remove
// this check once low-pass to band-pass transform is implemented.
if (~ isscalar (w))
error ("besself: band-pass and stop-band filters not yet implemented");
end
[rows_w colums_w] = size(w);
if (~ ((length (w) <= 2) & (rows_w == 1 | columns_w == 1)))
error ("besself: frequency must be given as WC or [WL, WH]");
elseif ((length (w) == 2) & (w(2) <= w(1)))
error ("besself: W(1) must be less than W(2)");
end
if (digital & ~ and ((w >= 0) & (w <= 1)))
error ("besself: and elements of W must be in the range [0,1]");
elseif (~ digital & ~ and (w >= 0))
error ("besself: and elements of W must be in the range [0,inf]");
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);
end
// 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);
end
// convert to the correct output form
if (nargout == 2)
// a = real (gain * poly (zero));
// b = real (poly (pole));
[a b] = zp2tf(zero, pole, gain);
elseif (nargout == 3)
a = zero;
b = pole;
c = gain;
else
// output ss results
// [a, b, c, d] = zp2ss (zero, pole, gain);
error("besself: yet not implemented in state-space form OR invalid number of o/p arguments")
end
endfunction
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