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Diffstat (limited to 'macros/butter.sci')
| -rw-r--r-- | macros/butter.sci | 201 |
1 files changed, 145 insertions, 56 deletions
diff --git a/macros/butter.sci b/macros/butter.sci index a11da7e..73cdb71 100644 --- a/macros/butter.sci +++ b/macros/butter.sci @@ -1,58 +1,147 @@ +// 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] = butter (n, w, varargin) -//This function generates a Butterworth filter. -//Calling Sequence -//[a, b] = butter (n, w) -//[a, b] = butter (n, w, "high") -//[a, b] = butter (n, [wl, wh]) -//[b, a] = butter (n, [wl, wh], "stop") -//[a, b, c] = butter (…) -//[a, b, c, d] = butter (…) -//[…] = butter (…, "s") -//Parameters -//n: positive integer value -//w: positive real value, w in the range [0,1] -//Description -//This is an Octave function. -//This function generates a Butterworth filter. Default is a discrete space (Z) filter. -//The third parameter takes in low or high, default value is low. The cutoff is pi*Wc radians. -//[b,a] = butter(n, [Wl, Wh]) indicates a band pass filter with edges pi*Wl and pi*Wh radians. -//[b,a] = butter(n, [Wl, Wh], ’stop’) indicates a band reject filter with edges pi*Wl and pi*Wh radians. -//[z,p,g] = butter(...) returns filter as zero-pole-gain rather than coefficients of the numerator and denominator polynomials. -//[...] = butter(...,’s’) returns a Laplace space filter, w can be larger than 1. -//[a,b,c,d] = butter(...) returns state-space matrices. -//Examples -//[a,b]=butter(3, 0.7) -//a = -// 0.37445 1.12336 1.12336 0.37445 -//b = -// 1.00000 1.16192 0.69594 0.13776 - -rhs = argn(2) -lhs = argn(1) -if(rhs>4 | rhs<2) -error("Wrong number of input arguments.") -end -if(lhs>4 | lhs<2) -error("Wrong number of output arguments.") -end - - select (rhs) - case 2 then - if (lhs==2) [a,b] = callOctave("butter",n, w) - elseif (lhs==3) [a,b,c] = callOctave("butter",n, w) - elseif (lhs==4) [a,b,c,d] = callOctave("butter",n, w) - end - case 3 then - if (lhs==2) [a,b] = callOctave("butter",n, w,varargin(1)) - elseif (lhs==3) [a,b,c] = callOctave("butter",n, w,varargin(1)) - elseif (lhs==4) [a,b,c,d] = callOctave("butter",n, w,varargin(1)) - end - case 4 then - if (lhs==2) [a,b] = callOctave("butter",n, w,varargin(1),varargin(2)) - elseif (lhs==3) [a,b,c] = callOctave("butter",n, w,varargin(1),varargin(2)) - elseif (lhs==4) [a,b,c,d] = callOctave("butter",n, w,varargin(1),varargin(2)) - end - end -endfunction - + //Butterworth filter design. + + //Calling Sequence + //[b, a] = butter (n, wc) + //[b, a] = butter (n, wc, "high") + //[b, a] = butter (n, [wl, wh]) + //[b, a] = butter (n, [wl, wh], "stop") + //[z, p, g] = butter (…) + //[…] = butter (…, "s") + + //Parameters + //n: positive integer value (order of filter) + //wc: positive real value, + // 1).Normalised digital 3dB cutoff frequency/frequencies for digital filter, in the range [0, 1] {dimensionless} + // 2).Analog 3dB cutoff frequency/frequencies for analog filter, in the range [0, Inf] {rad/sec} + + //Description + //This function generates a Butterworth filter. Default is a discrete space (z) or digital filter using Bilinear transformation from s to z plane. + //If second argument is scalar the third parameter takes in low or high, default value is low. The cutoff is pi*wc radians. + //[b,a] = butter(n, [wl, wh]) indicates a band pass filter with cutoffs pi*Wl and pi*wh radians. + //[b,a] = butter(n, [wl, wh], ’stop’) indicates a band reject filter with cutoffs pi*wl and pi*wh radians. + //[z,p,g] = butter(...) returns filter as zero-pole-gain rather than coefficients of the numerator and denominator polynomials. + //[...] = butter(...,’s’) returns a Laplace space filter,here cutoff(s) wc can be larger than 1 (rad/sec). + + //Examples + //[b a] = butter(4,0.3,"high") + //Output + // a = + // + // + // column 1 to 4 + // + // 1. - 1.5703989 1.2756133 - 0.4844034 + // + // column 5 + // + // 0.0761971 + // b = + // + // + // column 1 to 4 + // + // 0.2754133 - 1.1016532 1.6524797 - 1.1016532 + // + // column 5 + // + // 0.2754133 + + + funcprot(); + [nargout nargin] = argn(); + if (nargin > 4 | nargin < 2 | nargout > 4 | nargout < 2) + error("butter: Invalid number of input argument") + end + + // interpret the input parameters + if (~ (isscalar (n) & (n == fix (n)) & (n > 0))) + error ("butter: 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 ("butter: 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 ("butter: frequency must be given as WC or [WL, WH]"); + elseif ((length (w) == 2) & (w(2) <= w(1))) + error ("butter: W(1) must be less than W(2)"); + end + + if (digital & ~ and ((w >= 0) & (w <= 1))) + error ("butter: all elements of W must be in the range [0,1] for digital filter"); + elseif (~ digital & ~ and (w >= 0)) + error ("butter: all elements of W must be in the range [0,inf] for analog filter"); + 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 Butterworth filter + // source: Kuc + C = 1; // default cutoff frequency + pole = C * exp (1*%i * %pi * (2 * [1:n] + n - 1) / (2 * n)); + if (pmodulo (n, 2) == 1) + pole((n + 1) / 2) = -1; // pure real value at exp(%i*%pi) + end + zero = []; + gain = C^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("butter: yet not implemented in state-space form OR invalid number of o/p arguments") + end +endfunction |