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annotate scripts/signal/fftfilt.m @ 20614:10ec79b47808

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use new string_value method to handle value extraction errors * __voronoi__.cc, chol.cc, colamd.cc, fftw.cc: Use new string_value method.
author John W. Eaton <jwe@octave.org>
date Thu, 08 Oct 2015 18:15:56 -0400
parents f1d0f506ee78
children
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rev   line source
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4197fc428c7d maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1994-2015 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})
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21 ## @deftypefnx {Function File} {} fftfilt (@var{b}, @var{x}, @var{n})
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22 ## Filter @var{x} with the FIR filter @var{b} using the FFT.
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23 ##
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24 ## If @var{x} is a matrix, filter each column of the matrix.
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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 ## The FFT size must be an even power of 2 and must be greater than or equal to
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29 ## the length of @var{b}. If the specified @var{n} does not meet these
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30 ## criteria, it is automatically adjusted to the nearest value that does.
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31 ##
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32 ## @seealso{filter, filter2}
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33 ## @end deftypefn
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34
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35 ## Author: Kurt Hornik <Kurt.Hornik@wu-wien.ac.at>
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36 ## Created: 3 September 1994
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37 ## Adapted-By: jwe
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38
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39 function y = fftfilt (b, x, n)
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40
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41 ## If N is not specified explicitly, we do not use the overlap-add
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42 ## method at all because loops are really slow. Otherwise, we only
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43 ## ensure that the number of points in the FFT is the smallest power
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44 ## of two larger than N and length(b). This could result in length
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45 ## one blocks, but if the user knows better ...
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46
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47 if (nargin < 2 || nargin > 3)
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48 print_usage ();
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49 endif
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50
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51 transpose = (rows (x) == 1);
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52
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53 if (transpose)
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54 x = x.';
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55 endif
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56
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57 [r_x, c_x] = size (x);
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58 [r_b, c_b] = size (b);
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59
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60 if (! isvector (b))
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61 error ("fftfilt: B must be a vector");
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62 endif
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63
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64 if (ndims (x) != 2)
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65 error ("fftfilt: X must be a 1-D or 2-D array");
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66 endif
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67
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68 l_b = r_b * c_b;
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69 b = reshape (b, l_b, 1);
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70
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71 if (nargin == 2)
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72 ## Use FFT with the smallest power of 2 which is >= length (x) +
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73 ## length (b) - 1 as number of points ...
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74 n = 2 ^ nextpow2 (r_x + l_b - 1);
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75 B = fft (b, n);
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76 y = ifft (fft (x, n) .* B(:, ones (1, c_x)));
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77 else
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78 ## Use overlap-add method ...
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79 if (! (isscalar (n)))
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80 error ("fftfilt: N has to be a scalar");
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81 endif
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82 n = 2 ^ nextpow2 (max ([n, l_b]));
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83 L = n - l_b + 1;
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84 B = fft (b, n);
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85 B = B(:, ones (c_x,1));
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86 R = ceil (r_x / L);
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87 y = zeros (r_x, c_x);
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88 for r = 1:R;
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89 lo = (r - 1) * L + 1;
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90 hi = min (r * L, r_x);
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91 tmp = zeros (n, c_x);
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92 tmp(1:(hi-lo+1),:) = x(lo:hi,:);
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93 tmp = ifft (fft (tmp) .* B);
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94 hi = min (lo+n-1, r_x);
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95 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:);
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96 endfor
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97 endif
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98
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99 y = y(1:r_x, :);
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100
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101 ## Final cleanups:
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102
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103 ## - If both b and x are real, y should be real.
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104 ## - If b is real and x is imaginary, y should be imaginary.
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105 ## - If b is imaginary and x is real, y should be imaginary.
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106 ## - If both b and x are imaginary, y should be real.
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107 xisreal = all (imag (x) == 0);
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108 xisimag = all (real (x) == 0);
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109
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110 if (all (imag (b) == 0))
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111 y (:,xisreal) = real (y (:,xisreal));
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112 y (:,xisimag) = complex (real (y (:,xisimag)) * 0, imag (y (:,xisimag)));
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113 elseif (all (real (b) == 0))
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114 y (:,xisreal) = complex (real (y (:,xisreal)) * 0, imag (y (:,xisreal)));
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115 y (:,xisimag) = real (y (:,xisimag));
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116 endif
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117
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118 ## - If both x and b are integer in both real and imaginary
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119 ## components, y should be integer.
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120 if (! any (b - fix (b)))
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121 idx = find (! any (x - fix (x)));
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122 y (:, idx) = round (y (:, idx));
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123 endif
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124
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125 ## Transpose after cleanup, otherwise rounding fails.
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126 if (transpose)
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127 y = y.';
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128 endif
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129
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130 endfunction
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133 %!shared b, x, r
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135 %!test
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136 %! b = [1 1];
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137 %! x = [1, zeros(1,9)];
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138 %! assert (fftfilt (b, x ), [1 1 0 0 0 0 0 0 0 0] );
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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.' x.']), [1 1 0 0 0 0 0 0 0 0].'*[1 1]);
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143 %! 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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145 %!test
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146 %! r = sqrt (1/2) * (1+i);
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147 %! b = b*r;
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148 %! assert (fftfilt (b, x ), r*[1 1 0 0 0 0 0 0 0 0] , eps );
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149 %! assert (fftfilt (b, r*x), r*r*[1 1 0 0 0 0 0 0 0 0], 2*eps);
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150 %! assert (fftfilt (b, x.'), r*[1 1 0 0 0 0 0 0 0 0].', eps );
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152 %!test
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153 %! b = [1 1];
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154 %! x = zeros (10,3); x(1,1)=-1; x(1,2)=1;
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155 %! y0 = zeros (10,3); y0(1:2,1)=-1; y0(1:2,2)=1;
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156 %! y = fftfilt (b, x);
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157 %! assert (y0, y);
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158 %! y = fftfilt (b*i, x);
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159 %! assert (y0*i, y);
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160 %! y = fftfilt (b, x*i);
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161 %! assert (y0*i, y);
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162 %! y = fftfilt (b*i, x*i);
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163 %! assert (-y0, y);
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164 %! x = rand (10, 1);
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165 %! y = fftfilt (b, [x x*i]);
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166 %! assert (true, isreal (y(:,1)));
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167 %! assert (false, any (real (y(:,2))));
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169 %!test
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170 %! b = rand (10, 1);
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171 %! x = rand (10, 1);
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172 %! y0 = filter (b, 1, x);
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173 %! y = fftfilt (b, x);
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174 %! assert (y0, y, 16*eps);
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175 %! y0 = filter (b*i, 1, x*i);
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176 %! y = fftfilt (b*i, x*i);
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177 %! assert (y0, y, 16*eps);
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178
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179 %!test
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180 %! b = rand (10, 1) + i*rand (10, 1);
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181 %! x = rand (10, 1) + i*rand (10, 1);
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182 %! y0 = filter (b, 1, x);
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183 %! y = fftfilt (b, x);
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184 %! assert (y0, y, 55*eps);
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185
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186 ## Test input validation
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187 %!error fftfilt (1)
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188 %!error fftfilt (1, 2, 3, 4)
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189 %!error fftfilt (ones (2), 1)
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190 %!error fftfilt (2, ones (3,3,3))
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191 %!error fftfilt (2, 1, ones (2))
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192