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annotate scripts/signal/fftfilt.m @ 14138:72c96de7a403 stable

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maint: update copyright notices for 2012
author John W. Eaton <jwe@octave.org>
date Mon, 02 Jan 2012 14:25:41 -0500
parents 186c3b80ba54
children f3d52523cde1
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14138
72c96de7a403 maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1994-2012 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 3 of the License, or (at
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8 ## your option) 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, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} fftfilt (@var{b}, @var{x}, @var{n})
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21 ##
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22 ## With two arguments, @code{fftfilt} filters @var{x} with the FIR filter
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23 ## @var{b} using the FFT.
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24 ##
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25 ## Given the optional third argument, @var{n}, @code{fftfilt} uses the
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26 ## overlap-add method to filter @var{x} with @var{b} using an N-point FFT.
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27 ##
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28 ## If @var{x} is a matrix, filter each column of the matrix.
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29 ## @seealso{filter, filter2}
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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 (! isvector (b))
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58 error ("fftfilt: B must be a vector");
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59 endif
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60
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61 if (ndims (x) != 2)
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62 error ("fftfilt: X must be a 1-D or 2-D array");
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63 endif
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64
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65 l_b = r_b * c_b;
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66 b = reshape (b, l_b, 1);
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67
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68 if (nargin == 2)
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69 ## Use FFT with the smallest power of 2 which is >= length (x) +
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70 ## length (b) - 1 as number of points ...
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71 n = 2 ^ nextpow2 (r_x + l_b - 1);
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72 B = fft (b, n);
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73 y = ifft (fft (x, n) .* B(:, ones (1, c_x)));
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74 else
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75 ## Use overlap-add method ...
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76 if (! (isscalar (n)))
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77 error ("fftfilt: N has to be a scalar");
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78 endif
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79 n = 2 ^ nextpow2 (max ([n, l_b]));
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80 L = n - l_b + 1;
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81 B = fft (b, n);
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82 B = B(:, ones (c_x,1));
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83 R = ceil (r_x / L);
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84 y = zeros (r_x, c_x);
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85 for r = 1:R;
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86 lo = (r - 1) * L + 1;
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87 hi = min (r * L, r_x);
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88 tmp = zeros (n, c_x);
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89 tmp(1:(hi-lo+1),:) = x(lo:hi,:);
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90 tmp = ifft (fft (tmp) .* B);
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91 hi = min (lo+n-1, r_x);
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92 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:);
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93 endfor
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94 endif
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95
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96 y = y(1:r_x, :);
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97 if (transpose)
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98 y = y.';
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99 endif
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100
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101 ## Final cleanups: If both x and b are real, y should be real.
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102 ## If both x and b are integer, y should be integer.
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103
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104 if (isreal (b) && isreal (x))
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105 y = real (y);
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106 endif
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107 if (! any (b - fix (b)))
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108 idx = !any (x - fix (x));
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109 y(:, idx) = round (y(:, idx));
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110 endif
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111
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112 endfunction
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113
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114
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115 %!shared b, x, r
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116 %!test
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117 %! b = [1 1];
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118 %! x = [1, zeros(1,9)];
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119 %! assert(fftfilt(b, x ), [1 1 0 0 0 0 0 0 0 0] , eps);
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120 %! assert(fftfilt(b, x.'), [1 1 0 0 0 0 0 0 0 0].', eps);
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121 %! assert(fftfilt(b.',x ), [1 1 0 0 0 0 0 0 0 0] , eps);
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122 %! assert(fftfilt(b.',x.'), [1 1 0 0 0 0 0 0 0 0].', eps);
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123
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124 %!test
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125 %! r = sqrt(1/2) * (1+i);
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126 %! b = b*r;
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127 %! assert(fftfilt(b, x ), r*[1 1 0 0 0 0 0 0 0 0] , eps);
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128 %! assert(fftfilt(b, r*x), r*r*[1 1 0 0 0 0 0 0 0 0], eps);
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129 %! assert(fftfilt(b, x.'), r*[1 1 0 0 0 0 0 0 0 0].', eps);
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130
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131 %!test
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132 %! b = [1 1];
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133 %! x = zeros (10,3); x(1,1)=-1; x(1,2)=1;
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134 %! y0 = zeros (10,3); y0(1:2,1)=-1; y0(1:2,2)=1;
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135 %! y = fftfilt (b, x);
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136 %! assert (y,y0);
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137
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Rik <octave@nomad.inbox5.com>
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diff changeset
138 %!test
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
139 %! b = rand (10, 1);
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
140 %! x = rand (10, 1);
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
141 %! y0 = filter (b, 1, x);
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
142 %! y = filter (b, 1, x);
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
143 %! assert (y, y0);
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
144
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
145 %% Test input validation
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
146 %!error fftfilt (1)
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
147 %!error fftfilt (1, 2, 3, 4)
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
148 %!error fftfilt (ones (2), 1)
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
149 %!error fftfilt (2, ones (3,3,3))
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
150 %!error fftfilt (2, 1, ones (2))
186c3b80ba54 codesprint: Tests for fftfilt()
Rik <octave@nomad.inbox5.com>
parents: 12546
diff changeset
151