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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 [n, Wc] = buttord(Wp, Ws, Rp, Rs)
//Minimum filter order and 3dB cutoff frequency of a digital Butterworth filter with the desired response characteristics
//Calling Sequence
//n = buttord(Wp, Ws, Rp, Rs)
//[n, Wc] = buttord(Wp, Ws, Rp, Rs)
//Parameters
//Wp: scalar or vector of length 2 (passband edge(s) ), elements must be in the range [0,1]
//Ws: scalar or vector of length 2 (stopband edge(s) ), elements must be in the range [0,1]
//Rp: passband ripple in dB.
//Rs: stopband attenuation in dB.
//n: Minimum filter order satisfying specs
//Wc: 3dB cutoff frequency/frequencies
//Description.
//This function computes the minimum filter order of a Butterworth filter with the desired response characteristics.
//The filter frequency band edges are specified by the passband frequency wp and stopband frequency ws.
//Frequencies are normalized to the Nyquist frequency in the range [0,1].
//Rp is measured in decibels and is the allowable passband ripple, and Rs is also in decibels and is the minimum attenuation in the stop band.
//If ws>wp, the filter is a low pass filter. If wp>ws, the filter is a high pass filter.
//If wp and ws are vectors of length 2, then the passband interval is defined by wp the stopband interval is defined by ws.
//If wp is contained within the lower and upper limits of ws, the filter is a band-pass filter. If ws is contained within the lower and upper limits of wp the filter is a band-stop or band-reject filter.
//Examples
//Wp = 40/500 ;
//Ws = 150/500 ;
//[n, Wc] = buttord(Wp, Ws, 3, 60)
//Output :
// Wc =
//
// 0.0800376
// n =
//
// 5.
funcprot(0);
[nargout nargin] = argn();
if (nargin ~= 4)
error("buttord: invalid number of inputs");
else
validate_filter_bands ("buttord", Wp, Ws);
end
if (length (Wp) == 2)
warning ("buttord: seems to overdesign bandpass and bandreject filters");
end
T = 2;
// if high pass, reverse the sense of the test
stop = find(Wp > Ws);
Wp(stop) = 1-Wp(stop); // stop will be at most length 1, so no need to
Ws(stop) = 1-Ws(stop); // subtract from ones(1,length(stop))
// warp the target frequencies according to the bilinear transform
Ws = (2/T)*tan(%pi*Ws./T);
Wp = (2/T)*tan(%pi*Wp./T);
// compute minimum n which satisfies all band edge conditions
// the factor 1/length(Wp) is an artificial correction for the
// band pass/stop case, which otherwise significantly overdesigns.
qs = log(10^(Rs/10) - 1);
qp = log(10^(Rp/10) - 1);
n = ceil(max(0.5*(qs - qp)./log(Ws./Wp))/length(Wp));
// compute -3dB cutoff given Wp, Rp and n
Wc = exp(log(Wp) - qp/2/n);
// unwarp the returned frequency
Wc = atan(T/2*Wc)*T/%pi;
// if high pass, reverse the sense of the test
Wc(stop) = 1-Wc(stop);
endfunction
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