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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
// Author:[insert name]
// 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].
//
//
//Test cases:
////1.
//n=0:319;
//x=cos(%pi/4*n)+rand(size(n,"r"),"normal");
//[pxx,w]=periodogram(x,ones(1,320),256,2000,"onesided");
//plot2d(w,10*log10(pxx))
//xtitle('periodogram','frequency','magnitude(db)')
//xgrid()
//
//
[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,"r");
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 (~strcmpi (ran, "onesided"))
ran = 1;
elseif (~strcmpi (ran, "twosided"))
ran = 2;
elseif (~strcmpi (ran, "centered"))
error ('periodogram: centered ran type is not implemented');
else
ran = 2-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,length(x)/nfft), 2);
end
if (~ isempty (win))
n = sum(win.*conj(win));
end;
Pxx = (abs (fft (x))) .^ 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)
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
pxx = Pxx;
endfunction
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