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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] = cheby2 (n, rs, w, varargin)
//Chebyshev type II filter design with rs dB of stopband attenuation.
//Calling Sequence
//[b, a] = cheby2 (n, rs, ws)
//[b, a] = cheby2 (n, rs, ws, "high")
//[b, a] = cheby2 (n, rs, [wl, wh])
//[b, a] = cheby2 (n, rs, [wl, wh], "stop")
//[z, p, g] = cheby2 (…)
//[…] = cheby2 (…, "s")
//Parameters
//n: positive integer value (order of filter)
//rs: non negative scalar value (stopband attenuation in dB)
//ws: positive real value,
// 1).Normalised digital stopband edge(s) for digital filter, in the range [0, 1] {dimensionless}
// 2).Analog stopband edge(s) for analog filter, in the range [0, Inf] {rad/sec}
//Description
//This function generates a Chebyshev type II filter with rs dB of stopband attenuation.
//The fourth parameter takes in high or low, default value is low. The cutoff is pi*Wc radians.
//[b, a] = cheby2(n, Rp, [Wl, Wh]) indicates a band pass filter with edges pi*Wl and pi*Wh radians.
//[b, a] = cheby2(n, Rp, [Wl, Wh], ’stop’) indicates a band reject filter with edges pi*Wl and pi*Wh radians.
//[z, p, g] = cheby2(...) returns filter as zero-pole-gain rather than coefficients of the numerator and denominator polynomials.
//[...] = cheby2(...,’s’) returns a Laplace space filter, w can be larger than 1.
//Examples
//[z, p, g]=cheby2(2,5,0.7,"high")
//Output:
// g =
//
// 0.4752770
// p =
//
// - 0.3938806 + 0.5313815i - 0.3938806 - 0.5313815i
// z =
//
// - 0.3164543 - 0.9486078i - 0.3164543 + 0.9486078i
funcprot(0);
[nargout nargin] = argn();
if (nargin > 5 | nargin < 3 | nargout > 4 | nargout < 2)
error("cheby2: invalid number of inputs");
end
// interpret the input parameters
if (~ (isscalar (n) & (n == fix (n)) & (n > 0)))
error ("cheby2: filter order N must be a positive integer");
end
stop = %F;
digital = %T;
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 = %T;
case "pass"
stop = %F;
else
error ("cheby2: expected [high|stop] or [s|z]");
end
end
[rows_w columns_w] = size(w);
if (~ ((length (w) <= 2) & (rows_w == 1 | columns_w == 1)))
error ("cheby2: frequency must be given as WS or [WL, WH]");
elseif ((length (w) == 2) & (w(2) <= w(1)))
error ("cheby2: W(1) must be less than W(2)");
end
if (digital & ~ and ((w >= 0) & (w <= 1)))
error ("cheby2: all elements of W must be in the range [0,1]");
elseif (~ digital & ~ and (w >= 0))
error ("cheby2: all elements of W must be in the range [0,inf]");
end
if (~ (isscalar (rs) & or(type(rs) == [1 5 8]) & (rs >= 0)))
error ("cheby2: stopband attenuation RS must be a non-negative scalar");
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 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 (modulo (n, 2))
// drop theta==pi/2 since it results in a zero at infinity
zero = 1*%i * C ./ cos (theta([1:(n - 1) / 2, (n + 3) / 2:n]));
else
zero = 1*%i * C ./ cos (theta);
end
pole = C ./ (alpha.^2 + beta.^2) .* (alpha - 1*%i * 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);
end
// convert to the correct output form
if (nargout == 2)
[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("cheby2: yet not implemented in state-space form OR invalid number of o/p arguments")
end
endfunction
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