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1 ### Copyright (C) 1996 John W. Eaton |
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2 ### |
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3 ### This file is part of Octave. |
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4 ### |
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5 ### Octave is free software; you can redistribute it and/or modify it |
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6 ### under the terms of the GNU General Public License as published by |
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7 ### the Free Software Foundation; either version 2, or (at your option) |
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8 ### any later version. |
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9 ### |
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10 ### Octave is distributed in the hope that it will be useful, but |
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11 ### WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ### General Public License for more details. |
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14 ### |
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15 ### You should have received a copy of the GNU General Public License |
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16 ### along with Octave; see the file COPYING. If not, write to the Free |
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17 ### Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ### 02111-1307, USA. |
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19 |
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20 ## usage: fftfilt (b, x [, N]) |
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21 ## |
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22 ## y = fftfilt (b, x) filters x with the FIR filter b using the FFT. |
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23 ## y = fftfilt (b, x, N) uses the overlap-add method to filter x with |
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24 ## b using an N-point FFT. |
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25 |
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26 function y = fftfilt (b, x, N) |
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27 |
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28 ## Written by KH (Kurt.Hornik@ci.tuwien.ac.at) on Sep 3, 1994 |
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29 |
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30 ## Reference: Oppenheim & Schafer (1989). Discrete-time Signal |
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31 ## Processing (Chapter 8). Prentice-Hall. |
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32 |
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33 ## If N is not specified explicitly, we do not use the overlap-add |
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34 ## method at all because loops are really slow. Otherwise, we only |
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35 ## ensure that the number of points in the FFT is the smallest power |
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36 ## of two larger than N and length(b). This could result in length |
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37 ## one blocks, but if the user knows better ... |
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38 |
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39 if (nargin < 2 || nargin > 3) |
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40 usage (" fftfilt (b, x [, N])"); |
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41 endif |
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42 |
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43 [r_x, c_x] = size (x); |
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44 [r_b, c_b] = size (b); |
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45 if (! (min ([r_x, c_x]) == 1 || min ([r_b, c_b]) == 1)) |
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46 error ("fftfilt: both x and b should be vectors"); |
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47 endif |
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48 l_x = r_x * c_x; |
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49 l_b = r_b * c_b; |
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50 |
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51 if ((l_x == 1) && (l_b == 1)) |
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52 y = b * x; |
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53 return; |
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54 endif |
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55 |
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56 x = reshape (x, 1, l_x); |
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57 b = reshape (b, 1, l_b); |
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58 |
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59 if (nargin == 2) |
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60 ## Use FFT with the smallest power of 2 which is >= length (x) + |
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61 ## length (b) - 1 as number of points ... |
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62 N = 2^(ceil (log (l_x + l_b - 1) / log(2))); |
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63 y = ifft (fft (x, N) .* fft(b, N)); |
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64 else |
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65 ## Use overlap-add method ... |
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66 if !(is_scalar (N)) |
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67 error ("fftfilt: N has to be a scalar"); |
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68 endif |
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69 N = 2^(ceil (log (max ([N, l_b])) / log(2))); |
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70 L = N - l_b + 1; |
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71 B = fft (b, N); |
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72 R = ceil (l_x / L); |
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73 y = zeros (1, l_x); |
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74 for r = 1:R; |
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75 lo = (r - 1) * L + 1; |
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76 hi = min (r * L, l_x); |
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77 tmp = ifft (fft (x(lo:hi), N) .* B); |
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78 hi = min (lo+N-1, l_x); |
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79 y(lo:hi) = y(lo:hi) + tmp(1:(hi-lo+1)); |
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80 endfor |
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81 endif |
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82 |
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83 y = reshape (y(1:l_x), r_x, c_x); |
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84 |
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85 ## Final cleanups: if both x and b are real respectively integer, y |
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86 ## should also be |
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87 |
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88 if (! (any (imag (x)) || any (imag (b)))) |
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89 y = real (y); |
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90 endif |
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91 if (! (any (x - round (x)) || any (b - round (b)))) |
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92 y = round (y); |
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93 endif |
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94 |
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95 endfunction |
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96 |
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97 |
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100 |
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101 |
