annotate scripts/signal/fftfilt.m @ 17173:bb60b1bb47cf

view.m: Fix args undefined error when calling with two arguments
author Max Brister <max@2bass.com>
date Sat, 03 Aug 2013 17:23:44 -0600
parents b9ffacf34c2d
children d6499c14021c
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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 @var{n}-point
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27 ## FFT. The FFT size must be an even power of 2 and must be greater than
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28 ## or equal to the length of @var{b}. If the specified @var{n} does not
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29 ## meet these criteria, it is automatically adjusted to the nearest value
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30 ## that does.
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31 ##
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32 ## If @var{x} is a matrix, filter each column of the matrix.
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33 ## @seealso{filter, filter2}
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34 ## @end deftypefn
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35
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36 ## Author: Kurt Hornik <Kurt.Hornik@wu-wien.ac.at>
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37 ## Created: 3 September 1994
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38 ## Adapted-By: jwe
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39
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40 function y = fftfilt (b, x, n)
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41
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42 ## If N is not specified explicitly, we do not use the overlap-add
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43 ## method at all because loops are really slow. Otherwise, we only
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44 ## ensure that the number of points in the FFT is the smallest power
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45 ## of two larger than N and length(b). This could result in length
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46 ## one blocks, but if the user knows better ...
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47
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48 if (nargin < 2 || nargin > 3)
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49 print_usage ();
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50 endif
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51
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52 transpose = (rows (x) == 1);
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53
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54 if (transpose)
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55 x = x.';
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56 endif
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57
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58 [r_x, c_x] = size (x);
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59 [r_b, c_b] = size (b);
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60
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61 if (! isvector (b))
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62 error ("fftfilt: B must be a vector");
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63 endif
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64
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65 if (ndims (x) != 2)
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66 error ("fftfilt: X must be a 1-D or 2-D array");
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67 endif
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68
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69 l_b = r_b * c_b;
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70 b = reshape (b, l_b, 1);
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71
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72 if (nargin == 2)
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73 ## Use FFT with the smallest power of 2 which is >= length (x) +
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74 ## length (b) - 1 as number of points ...
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75 n = 2 ^ nextpow2 (r_x + l_b - 1);
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76 B = fft (b, n);
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77 y = ifft (fft (x, n) .* B(:, ones (1, c_x)));
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78 else
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79 ## Use overlap-add method ...
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80 if (! (isscalar (n)))
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81 error ("fftfilt: N has to be a scalar");
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82 endif
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83 n = 2 ^ nextpow2 (max ([n, l_b]));
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84 L = n - l_b + 1;
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85 B = fft (b, n);
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86 B = B(:, ones (c_x,1));
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87 R = ceil (r_x / L);
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88 y = zeros (r_x, c_x);
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89 for r = 1:R;
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90 lo = (r - 1) * L + 1;
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91 hi = min (r * L, r_x);
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92 tmp = zeros (n, c_x);
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93 tmp(1:(hi-lo+1),:) = x(lo:hi,:);
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94 tmp = ifft (fft (tmp) .* B);
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95 hi = min (lo+n-1, r_x);
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96 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:);
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97 endfor
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98 endif
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99
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100 y = y(1:r_x, :);
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101
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102 ## Final cleanups:
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103
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104 ## - If both b and x are real, y should be real.
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105 ## - If b is real and x is imaginary, y should be imaginary.
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106 ## - If b is imaginary and x is real, y should be imaginary.
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107 ## - If both b and x are imaginary, y should be real.
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108 xisreal = all (imag (x) == 0);
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109 xisimag = all (real (x) == 0);
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110
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111 if (all (imag (b) == 0))
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112 y (:,xisreal) = real (y (:,xisreal));
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113 y (:,xisimag) = complex (real (y (:,xisimag)) * 0, imag (y (:,xisimag)));
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114 elseif (all (real (b) == 0))
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115 y (:,xisreal) = complex (real (y (:,xisreal)) * 0, imag (y (:,xisreal)));
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116 y (:,xisimag) = real (y (:,xisimag));
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117 endif
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118
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119 ## - If both x and b are integer in both real and imaginary
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120 ## components, y should be integer.
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121 if (! any (b - fix (b)))
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122 idx = find (! any (x - fix (x)));
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123 y (:, idx) = round (y (:, idx));
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124 endif
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125
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126 ## Transpose after cleanup, otherwise rounding fails.
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127 if (transpose)
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128 y = y.';
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129 endif
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130
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131 endfunction
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132
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134 %!shared b, x, r
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135
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136 %!test
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137 %! b = [1 1];
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138 %! x = [1, zeros(1,9)];
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139 %! assert (fftfilt (b, x ), [1 1 0 0 0 0 0 0 0 0] );
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140 %! assert (fftfilt (b, x.'), [1 1 0 0 0 0 0 0 0 0].');
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141 %! assert (fftfilt (b.',x ), [1 1 0 0 0 0 0 0 0 0] );
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142 %! assert (fftfilt (b.',x.'), [1 1 0 0 0 0 0 0 0 0].');
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143 %! assert (fftfilt (b, [x.' x.']), [1 1 0 0 0 0 0 0 0 0].'*[1 1]);
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144 %! assert (fftfilt (b, [x.'+2*eps x.']) == [1 1 0 0 0 0 0 0 0 0].'*[1 1], [false(10, 1) true(10, 1)]);
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146 %!test
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147 %! r = sqrt (1/2) * (1+i);
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148 %! b = b*r;
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149 %! assert (fftfilt (b, x ), r*[1 1 0 0 0 0 0 0 0 0] , eps );
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150 %! assert (fftfilt (b, r*x), r*r*[1 1 0 0 0 0 0 0 0 0], 2*eps);
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151 %! assert (fftfilt (b, x.'), r*[1 1 0 0 0 0 0 0 0 0].', eps );
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153 %!test
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154 %! b = [1 1];
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155 %! x = zeros (10,3); x(1,1)=-1; x(1,2)=1;
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156 %! y0 = zeros (10,3); y0(1:2,1)=-1; y0(1:2,2)=1;
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157 %! y = fftfilt (b, x);
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158 %! assert (y0, y);
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159 %! y = fftfilt (b*i, x);
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160 %! assert (y0*i, y);
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161 %! y = fftfilt (b, x*i);
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162 %! assert (y0*i, y);
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163 %! y = fftfilt (b*i, x*i);
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164 %! assert (-y0, y);
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165 %! x = rand (10, 1);
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166 %! y = fftfilt (b, [x x*i]);
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167 %! assert (true, isreal (y(:,1)));
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168 %! assert (false, any (real (y(:,2))));
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170 %!test
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171 %! b = rand (10, 1);
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172 %! x = rand (10, 1);
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173 %! y0 = filter (b, 1, x);
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174 %! y = fftfilt (b, x);
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175 %! assert (y0, y, 16*eps);
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176 %! y0 = filter (b*i, 1, x*i);
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177 %! y = fftfilt (b*i, x*i);
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178 %! assert (y0, y, 16*eps);
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179
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180 %!test
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181 %! b = rand (10, 1) + i*rand (10, 1);
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182 %! x = rand (10, 1) + i*rand (10, 1);
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183 %! y0 = filter (b, 1, x);
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184 %! y = fftfilt (b, x);
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185 %! assert (y0, y, 55*eps);
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187 %% Test input validation
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188 %!error fftfilt (1)
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189 %!error fftfilt (1, 2, 3, 4)
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190 %!error fftfilt (ones (2), 1)
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191 %!error fftfilt (2, ones (3,3,3))
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192 %!error fftfilt (2, 1, ones (2))
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193