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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % DFT Compute discrete fourier transform at a given frequency
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % DFT Compute discrete fourier transform at a given frequency
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % It is defined as
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % X(f) = T*sum(x(t)*exp(-1i.*2.*pi.*f.*T.*t))|t=0,...,N-1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % where T is the sampling time
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % CALL
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % Gf = utils.math.dft(gt,f,T)
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11 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % INPUT
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13 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % - gt, input data series, Nx1 double
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % - f, a frequency point in Hz, 1x1 double
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16 % - T, sampling time in seconds, 1x1 double
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17 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % REFERENCES
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19 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % D. B. Percival and A. T. Walden, Spectral Analysis for Physical
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % Applications (Cambridge University Press, Cambridge, 1993) p 108.
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22 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % L Ferraioli 09-03-2011
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24 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % $Id: dft.m,v 1.2 2011/03/29 15:36:43 luigi Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 function Gf = dft(gt,f,T)
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28
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29 [nn,mm] = size(gt);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 if nn<mm % willing to work with columns
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31 gt = gt.';
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32 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 N = numel(gt);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 t = 0:N-1;
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35
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 ar = exp(-1i.*2.*pi.*f.*T.*t);
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37
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38 Gf = T*(ar*gt);
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39
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40
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41 end