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Diffstat (limited to 'macros/cheby1.sci')
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1 files changed, 147 insertions, 57 deletions
diff --git a/macros/cheby1.sci b/macros/cheby1.sci index 52ff1ad..272f7f9 100644 --- a/macros/cheby1.sci +++ b/macros/cheby1.sci @@ -1,59 +1,149 @@ +// 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] = cheby1 (n, rp, w, varargin) -//This function generates a Chebyshev type I filter with rp dB of passband ripple. -//Calling Sequence -//[a, b] = cheby1 (n, rp, w) -//[a, b] = cheby1 (n, rp, w, "high") -//[a, b] = cheby1 (n, rp, [wl, wh]) -//[a, b] = cheby1 (n, rp, [wl, wh], "stop") -//[a, b, c] = cheby1 (…) -//[a, b, c, d] = cheby1 (…) -//[…] = cheby1 (…, "s") -//Parameters -//n: positive integer value -//rp: non negative scalar value -//w: vector, all elements must be in the range [0,1] -//Description -//This is an Octave function. -//This function generates a Chebyshev type I filter with rp dB of passband ripple. -//The fourth parameter takes in high or low, default value is low. The cutoff is pi*Wc radians. -//[b, a] = cheby1(n, Rp, [Wl, Wh]) indicates a band pass filter with edges pi*Wl and pi*Wh radians. -//[b, a] = cheby1(n, Rp, [Wl, Wh], ’stop’) indicates a band reject filter with edges pi*Wl and pi*Wh radians. -//[z, p, g] = cheby1(...) returns filter as zero-pole-gain rather than coefficients of the numerator and denominator polynomials. -//[...] = cheby1(...,’s’) returns a Laplace space filter, w can be larger than 1. -//[a,b,c,d] = cheby1(...) returns state-space matrices. -//Examples -//[a,b,c]=cheby1(2,6,0.7,"high") -//a = -// 1 1 -//b = -// -0.62915 + 0.55372i -0.62915 - 0.55372i -//c = 0.055649 - -rhs = argn(2) -lhs = argn(1) -[rows,columns] = size(w) -if(rhs>5 | rhs<3) -error("Wrong number of input arguments.") -end -if(lhs>4 | lhs<2) -error("Wrong number of output arguments.") -end - - select (rhs) - case 3 then - if (lhs==2) [a,b] = callOctave("cheby1",n, rp, w) - elseif (lhs==3) [a,b,c] = callOctave("cheby1",n, rp, w) - elseif (lhs==4) [a,b,c,d] = callOctave("cheby1",n, rp, w) - end - case 4 then - if (lhs==2) [a,b] = callOctave("cheby1",n, rp, w, varargin(1)) - elseif (lhs==3) [a,b,c] = callOctave("cheby1",n, rp, w, varargin(1)) - elseif (lhs==4) [a,b,c,d] = callOctave("cheby1",n, rp, w, varargin(1)) - end - case 5 then - if (lhs==2) [a,b] = callOctave("cheby1",n, rp, rs, w, varargin(1), varargin(2)) - elseif (lhs==3) [a,b,c] = callOctave("cheby1",n, rp, rs, w, varargin(1), varargin(2)) - elseif (lhs==4) [a,b,c,d] = callOctave("cheby1",n, rp, rs, w, varargin(1), varargin(2)) - end - end + //Chebyshev type I filter design with rp dB of passband ripple. + + //Calling Sequence + //[b, a] = cheby1 (n, rp, wp) + //[b, a] = cheby1 (n, rp, wp, "high") + //[b, a] = cheby1 (n, rp, [wl, wh]) + //[b, a] = cheby1 (n, rp, [wl, wh], "stop") + //[z, p, g] = cheby1 (…) + //[…] = cheby1 (…, "s") + + //Parameters + //n: positive integer value (order of filter) + //rp: non negative scalar value (passband ripple) + //wp: positive real value, + // 1).Normalised digital passband edge(s) for digital filter, in the range [0, 1] {dimensionless} + // 2).Analog passband edge(s) for analog filter, in the range [0, Inf] {rad/sec} + + //Description + //This function generates a Chebyshev type I filter with rp dB of passband ripple. + //if second parameter is scalar the fourth parameter takes in high or low, default value is low. The cutoff is pi*Wc radians. + //[b, a] = cheby1(n, Rp, [Wl, Wh]) indicates a band pass filter with edges pi*Wl and pi*Wh radians. + //[b, a] = cheby1(n, Rp, [Wl, Wh], ’stop’) indicates a band reject filter with edges pi*Wl and pi*Wh radians. + //[z, p, g] = cheby1(...) returns filter as zero-pole-gain rather than coefficients of the numerator and denominator polynomials. + //[...] = cheby1(...,’s’) returns a Laplace space filter, w can be larger than 1 rad/sec. + + //Examples + //[z, p, k]=cheby1(2,6,0.7,"high") + // k = + // + // 0.0556491 + // p = + // + // - 0.6291539 + 0.5537247i - 0.6291539 - 0.5537247i + // z = + // + // 1. 1. + + funcprot(0); + [nargout nargin] = argn(); + + if (nargin > 5 | nargin < 3 | nargout > 4 | nargout < 2) + error("cheby1: invalid number of inputs"); + end + + // interpret the input parameters + if (~ (isscalar (n) & (n == fix (n)) & (n > 0))) + error ("cheby1: 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 ("cheby1: 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 ("cheby1: frequency must be given as WP or [WL, WH]"); + elseif ((length (w) == 2) & (w(2) <= w(1))) + error ("cheby1: W(1) must be less than W(2)"); + end + + if (digital & ~ and ((w >= 0) & (w <= 1))) + error ("cheby1: all elements of W must be in the range [0,1]"); + elseif (~ digital & ~ and (w >= 0)) + error ("cheby1: all elements of W must be in the range [0,inf]"); + end + + if (~ (isscalar (rp) & or(type (rp) == [1 5 8]) & (rp >= 0))) + error ("cheby1: passband ripple RP 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 1 filter + C = 1; // default cutoff frequency + epsilon = sqrt (10^(rp / 10) - 1); + v0 = asinh (1 / epsilon) / n; + pole = exp (1*%i * %pi * [-(n - 1):2:(n - 1)] / (2 * n)); + pole = -sinh (v0) * real (pole) + 1*%i * 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 (modulo (n, 2) == 0) + gain = gain / 10^(rp / 20); + end + + + // 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("cheby1: yet not implemented in state-space form OR invalid number of o/p arguments") + end + endfunction |