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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 % COMPUTEDFT Computes DFT using FFT or Goertzel
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 % This function is used to calculate the DFT of a signal using the FFT
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % or the Goertzel algorithm.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % [XX,F] = COMPUTEDFT(XIN,NFFT) where NFFT is a scalar and computes the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % DFT XX using FFT. F is the frequency points at which the XX is
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % computed and is of length NFFT.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % [XX,F] = COMPUTEDFT(XIN,F) where F is a vector with atleast two
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % elements computes the DFT XX using the Goertzel algorithm.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % [XX,F] = COMPUTEDFT(...,Fs) returns the frequency vector F (in hz)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % where Fs is the sampling frequency
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % Inputs:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % XIN is the input signal
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % NFFT if a scalar corresponds to the number of FFT points used to
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % calculate the DFT using FFT.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % NFFT if a vector corresponds to the frequency points at which the DFT
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % is calculated using goertzel.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % FS is the sampling frequency
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % A direct copy of MATLAB's function for LTPDA
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % M Hewitson 08-05-08
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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 % $Id: computeDFT.m,v 1.2 2008/08/01 13:19:42 ingo Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % Copyright 2006 The MathWorks, Inc.
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31
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 % [1] Oppenheim, A.V., and R.W. Schafer, Discrete-Time Signal Processing,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 % Prentice-Hall, Englewood Cliffs, NJ, 1989, pp. 713-718.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 % [2] Mitra, S. K., Digital Signal Processing. A Computer-Based Approach.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 % 2nd Ed. McGraw-Hill, N.Y., 2001.
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36
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 function [Xx,f] = computeDFT(xin,nfft,varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 error(nargchk(2,3,nargin,'struct'));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 if nargin > 2,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 Fs = varargin{1};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 Fs = 2*pi;
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44 end
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45
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 nx = size(xin,1);
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47
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 if length(nfft) > 1,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 isfreqVector = true;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 isfreqVector = false;
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52 end
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53
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 if ~isfreqVector,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 [Xx,f] = computeDFTviaFFT(xin,nx,nfft,Fs);
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56 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 [Xx,f] = computeDFTviaGoertzel(xin,nfft,Fs);
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58 end
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59
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60 end
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61
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 %-------------------------------------------------------------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 function [Xx,f] = computeDFTviaFFT(xin,nx,nfft,Fs)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 % Use FFT to compute raw STFT and return the F vector.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 % Handle the case where NFFT is less than the segment length, i.e., "wrap"
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 % the data as appropriate.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68 xin_ncol = size(xin,2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 xw = zeros(nfft,xin_ncol);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 if nx > nfft,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 for j = 1:xin_ncol,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 xw(:,j) = datawrap(xin(:,j),nfft);
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73 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 xw = xin;
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76 end
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77
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 Xx = fft(xw,nfft);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 f = psdfreqvec('npts',nfft,'Fs',Fs);
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80 end
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81
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 %--------------------------------------------------------------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 function [Xx,f] = computeDFTviaGoertzel(xin,freqvec,Fs)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 % Use Goertzel to compute raw DFT and return the F vector.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 f = freqvec(:);
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87 f = mod(f,Fs); % 0 <= f < = Fs
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 nfld = floor(freqvec(:)/Fs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 xm = size(xin,1); % NFFT
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90
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 % Indices used by the Goertzel function (see equation 11.1 pg. 755 of [2])
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 fscaled = f/Fs*xm+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 k = round(fscaled);
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94
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 % shift for each frequency from default xm length grid
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 deltak = fscaled-k;
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97
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 tempk = k;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 % If k > xm, fold over to the 1st bin
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 k(tempk > xm) = 1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 nfld = nfld + (tempk > xm); % Make nfld reflect fold in k because of round
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102
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 n = (0:xm-1)';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 Xx = zeros(size(k,1),size(xin,2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 for kindex = 1:length(k)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 % We need to evaluate the DFT at the requested frequency instead of a
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 % neighboring frequency that lies on the grid obtained with xm number
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108 % of points in the 0 to fs range. We do that by giving a complex phase
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 % to xin equal to the offset from the frequency to its nearest neighbor
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 % on the grid. This phase translates into a shift in the DFT by the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111 % same amount. The Xx(k) then is the DFT at (k+deltak).
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112
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Daniele Nicolodi <nicolodi@science.unitn.it>
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113 % apply kernal to xin so as to evaluate DFT at k+deltak)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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114 kernel = exp(-j*2*pi*deltak(kindex)/xm*n);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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115 xin_phaseshifted = xin.*repmat(kernel,1,size(xin,2));
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116
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117 Xx(kindex,:) = goertzel(xin_phaseshifted,k(kindex));
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118 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 % DFT computed at exactly the frequencies it was requested for
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121 f = freqvec(:);
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122 end
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123
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124