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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
// Last Modified on : Feb 2024
// Organization: FOSSEE, IIT Bombay
// Email: toolbox@scilab.in
function [pxx, f] = periodogram (x, varargin)
//Calling Sequence:
//[PXX, F] = periodogram (X, WIN, NFFT, FS)
//[PXX, F] = periodogram (..., "RANGE")
// The possible inputs are:
//
// X
//
// data vector. If X is real-valued a one-sided spectrum is
// estimated. If X is complex-valued, or "RANGE" specifies
// "twosided", the full spectrum is estimated.
//
// WIN
// window weight data. If window is empty or unspecified a
// default rectangular window is used. Otherwise, the window is
// applied to the signal ('X .* WIN') before computing the
// periodogram. The window data must be a vector of the same
// length as X.
//
// NFFT
// number of frequency bins. The default is 256 or the next
// higher power of 2 greater than the length of X ('max (256,
// 2.^nextpow2 (length (x)))'). If NFFT is greater than the
// length of the input then X will be zero-padded to the length
// of NFFT.
//
// FS
// sampling rate. The default is 1.
//
// RANGE
// range of spectrum. "onesided" computes spectrum from
// [0..nfft/2+1]. "twosided" computes spectrum from [0..nfft-1].
//
//
// Dependencies
// hamming fft1
[nargout,nargin]=argn();
// check input arguments
if (nargin < 1 | nargin > 5)
error("wrong no. of input arguments")
end
nfft = [];
fs = [];
ran = "";
win = [];
j = 2;
for k = 1:length (varargin)
if (type (varargin(k))==10)
ran = varargin(k);
else
select (j)
case 2
win = varargin(k);
case 3
nfft = varargin(k);
case 4
fs = varargin(k);
end
j=j+1;
end
end
if (~ isvector (x))
error ("periodogram: X must be a real or complex vector");
end
x = x(:); // Use column vectors from now on
n = size(x,1);
if (~isempty (win))
if (~ isvector (win) | length (win) ~= n)
error ("periodogram: WIN must be a vector of the same length as X");
end
win = win(:);
x =x.* win;
else
win=window("re",length(x));
win=win(:);
x=x.*win;
end
if (isempty (nfft))
nfft = max (256, 2.^nextpow2 (n));
elseif (~ isscalar (nfft))
error ("periodogram: NFFT must be a scalar");
end
use_w_freq = isempty (fs);
if (~use_w_freq & ~ isscalar (fs))
error ("periodogram: FS must be a scalar");
end
if (~strcmp (ran, "onesided"))
ran = 1;
elseif (~strcmp (ran, "twosided"))
ran = 2;
elseif (~strcmp (ran, "centered"))
error ('periodogram: centered ran type is not implemented');
else
ran = 2 - double(isreal (x));
end
// compute periodogram
if (n > nfft)
Pxx = 0;
rr = modulo(length(x), nfft);
if (rr)
x = [x(:); zeros(nfft-rr, 1)];
end
x = sum (matrix (x, nfft,-1), 2);
end
if (~ isempty (win))
n = sum(win.*conj(win));
end;
Pxx = (abs (fft1 (x,nfft))) .^ 2 / n;
if (use_w_freq)
Pxx =Pxx/(2*%pi);
else
Pxx =Pxx/fs;
end
// generate output arguments
if (ran == 1) // onesided
if (modulo(nfft,2)==0) // nfft is even
psd_len = (nfft/2)+1;
Pxx = Pxx(1:psd_len) + [0; Pxx(nfft:-1:psd_len+1); 0];
else // nfft is odd
psd_len = (nfft+1)/2;
Pxx = Pxx(1:psd_len) + [0; Pxx(nfft:-1:psd_len+1)];
end
end
//if (nargout() ~= 1) FIXME: fix nargout
if (ran == 1)
f = (0:nfft/2)' / nfft;
elseif (ran == 2)
f = (0:nfft-1)' / nfft;
end
if (use_w_freq)
f =f* 2*%pi; // generate w=2*pi*f
else
f =f* fs;
end
//end
if (nargout() ~= 2)
if (use_w_freq)
plot (f/(2*%pi), 10*log10 (Pxx));
xlabel ("normalized frequency [x pi rad]");
ylabel ("Power density [dB/rad/sample]");
else
plot (f, 10*log10 (Pxx));
xlabel ("frequency [Hz]");
ylabel ("Power density [dB/Hz]");
end
title ("Periodogram Power Spectral Density Estimate");
end
pxx = Pxx;
endfunction
/*
pi = %pi; // ezecute on scilab only
t = 0:0.01:1;
x = sin(2*pi*10*t);
periodogram(x);
x = complex(0:0.01:1, 0:0.01:1);
periodogram(x);
x = cos(0:0.01:1);
win = hamming(101);
periodogram(x, win);
x = tan(0:0.01:1);
nfft = 512;
periodogram(x, [], nfft);
t = 0:0.01:1;
x = sin(2*pi*10*t);
Fs = 100;
periodogram(x, [], [], Fs)
x = sin(0:0.01:1);
periodogram(x, [], [], [], 'onesided');
x = sin(0:0.01:1);
periodogram(x, [], [], [], 'twosided')
Fs = 1000;
t = 0:1/Fs:1-1/Fs;
f0 = 100;
x = sin(2*pi*f0*t);
[Pxx, f] = periodogram(x, [], [], Fs);
[_, idx] = max(Pxx);
detected_freq = f(idx);
// Test error : invalid window length
x = randn(100,1);
win = hamming(50);
periodogram(x, win)
// Test invalid nfft (negative)
periodogram(x, [], -256)
*/
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