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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: Abinash Singh Under FOSSEE Internship
// Date of Modification: 3 Feb 2024
// Organization: FOSSEE, IIT Bombay
// Email: toolbox@scilab.in
function [zero, pole, gain]=besselap(n)
//Bessel analog filter prototype.
//Calling Sequence
//[zero, pole, gain] = besselap(n)
//zero = besselap(n)
//Parameters
//n: Filter Order
//zero: Zeros
//pole: Poles
//gain: Gain
//Description
//It Return bessel analog filter prototype of nth order.
//Examples
//[zero, pole, gain] = besselap (5)
//Output :
// gain =
//
// 1.
// pole =
//
// - 0.5905759 + 0.9072068i
// - 0.5905759 - 0.9072068i
// - 0.9264421
// - 0.8515536 + 0.4427175i
// - 0.8515536 - 0.4427175i
// zero =
//
// []
// Dependencies
// prepad
funcprot(0);
[nargout, nargin] = argn() ;
if (nargin>1 | nargin<1)
error("besselap : wrong number of input argument")
end
// interpret the input parameters
if (~(length(n)==1 & n == round(n) & n > 0))
error ("besselap: filter order n must be a positive integer");
end
p0=1;
p1=[1 1];
for nn=2:n
px=(2*nn-1)*p1;
py=[p0 0 0];
px=prepad(px,max(length(px),length(py)));
py=prepad(py,length(px));
p0=p1;
p1=px+py;
end
// p1 now contains the reverse bessel polynomial for n
// scale it by replacing s->s/w0 so that the gain becomes 1
p1=p1.*p1(length(p1)).^((length(p1)-1:-1:0)/(length(p1)-1));
zero=[];
pole=roots(p1);
gain=1;
endfunction
/*
Note : The function is tested with Octave's outputs as a reference.
# all passed
[zero, pole, gain] = besselap (1)
[zero, pole, gain] = besselap (2)
[zero, pole, gain] = besselap (7)
[zero, pole, gain] = besselap (13)
[zero, pole, gain] = besselap (43)
*/
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