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1 ## Copyright (C) 1994, 1995, 1996, 1997, 1999, 2000, 2002, 2005, 2006, |
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2 ## 2007 John W. Eaton |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} fftfilt (@var{b}, @var{x}, @var{n}) |
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22 ## |
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23 ## With two arguments, @code{fftfilt} filters @var{x} with the FIR filter |
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24 ## @var{b} using the FFT. |
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25 ## |
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26 ## Given the optional third argument, @var{n}, @code{fftfilt} uses the |
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27 ## overlap-add method to filter @var{x} with @var{b} using an N-point FFT. |
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28 ## |
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29 ## If @var{x} is a matrix, filter each column of the matrix. |
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30 ## @end deftypefn |
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31 |
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32 ## Author: Kurt Hornik <Kurt.Hornik@wu-wien.ac.at> |
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33 ## Created: 3 September 1994 |
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34 ## Adapted-By: jwe |
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35 |
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36 function y = fftfilt (b, x, N) |
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37 |
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38 ## If N is not specified explicitly, we do not use the overlap-add |
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39 ## method at all because loops are really slow. Otherwise, we only |
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40 ## ensure that the number of points in the FFT is the smallest power |
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41 ## of two larger than N and length(b). This could result in length |
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42 ## one blocks, but if the user knows better ... |
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43 |
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44 if (nargin < 2 || nargin > 3) |
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45 print_usage (); |
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46 endif |
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47 |
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48 transpose = (rows (x) == 1); |
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49 |
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50 if (transpose) |
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51 x = x.'; |
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52 endif |
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53 |
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54 [r_x, c_x] = size (x); |
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55 [r_b, c_b] = size (b); |
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56 |
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57 if min ([r_b, c_b]) != 1 |
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58 error ("fftfilt: b should be a vector"); |
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59 endif |
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60 |
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61 l_b = r_b * c_b; |
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62 b = reshape (b, l_b, 1); |
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63 |
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64 if (nargin == 2) |
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65 ## Use FFT with the smallest power of 2 which is >= length (x) + |
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66 ## length (b) - 1 as number of points ... |
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67 N = 2 ^ (ceil (log (r_x + l_b - 1) / log (2))); |
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68 B = fft (b, N); |
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69 y = ifft (fft (x, N) .* B(:,ones (1, c_x))); |
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70 else |
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71 ## Use overlap-add method ... |
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72 if (! (isscalar (N))) |
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73 error ("fftfilt: N has to be a scalar"); |
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74 endif |
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75 N = 2 ^ (ceil (log (max ([N, l_b])) / log (2))); |
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76 L = N - l_b + 1; |
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77 B = fft (b, N); |
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78 B = B(:,ones (c_x,1)); |
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79 R = ceil (r_x / L); |
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80 y = zeros (r_x, c_x); |
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81 for r = 1:R; |
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82 lo = (r - 1) * L + 1; |
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83 hi = min (r * L, r_x); |
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84 tmp = zeros (N, c_x); |
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85 tmp(1:(hi-lo+1),:) = x(lo:hi,:); |
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86 tmp = ifft (fft (tmp) .* B); |
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87 hi = min (lo+N-1, r_x); |
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88 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:); |
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89 endfor |
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90 endif |
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91 |
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92 y = y(1:r_x,:); |
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93 if (transpose) |
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94 y = y.'; |
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95 endif |
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96 |
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97 ## Final cleanups: if both x and b are real respectively integer, y |
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98 ## should also be |
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99 |
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100 if (isreal (b) && isreal (x)) |
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101 y = real (y); |
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102 endif |
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103 if (! any (b - round (b))) |
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104 idx = !any (x - round (x)); |
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105 y(:,idx) = round (y(:,idx)); |
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106 endif |
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107 |
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108 endfunction |
