annotate scripts/signal/fftfilt.m @ 30330:01de0045b2e3

maint: Shorten some long lines to <= 80 characters (bug #57599) * audiorecorder.m, disable_diagonal_matrix.m, disable_permutation_matrix.m, disable_range.m, atan2d.m, accumdim.m, bitcmp.m, blkdiag.m, cplxpair.m, dblquad.m, integral2.m, integral3.m, interp2.m, interpn.m, logspace.m, delaunayn.m, griddata3.m, imread.m, genvarname.m, strread.m, nthargout.m, parseparams.m, lsqnonneg.m, qp.m, sqp.m, material.m, __gnuplot_legend__.m, plot.m, __gnuplot_drawnow__.m, polygcd.m, polyvalm.m, setdiff.m, fftfilt.m, eigs.m, betainc.m, cosint.m, factor.m, gallery.m, toeplitz.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, iqr.m, kurtosis.m, quantile.m, bin2dec.m, isstrprop.m, mat2str.m, strchr.m, strsplit.m, __have_feature__.m, datenum.m, datevec.m, eomday.m, weboptions.m: maint: Shorten some long lines to <= 80 characters.
author Rik <rik@octave.org>
date Tue, 23 Nov 2021 13:28:34 -0800
parents 7854d5752dd2
children 796f54d4ddbf
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 1994-2021 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {} fftfilt (@var{b}, @var{x})
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28 ## @deftypefnx {} {} fftfilt (@var{b}, @var{x}, @var{n})
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29 ## Filter @var{x} with the FIR filter @var{b} using the FFT.
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30 ##
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31 ## If @var{x} is a matrix, filter each column of the matrix.
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32 ##
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33 ## Given the optional third argument, @var{n}, @code{fftfilt} uses the
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34 ## overlap-add method to filter @var{x} with @var{b} using an N-point FFT@.
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35 ## The FFT size must be an even power of 2 and must be greater than or equal to
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36 ## the length of @var{b}. If the specified @var{n} does not meet these
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37 ## criteria, it is automatically adjusted to the nearest value that does.
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38 ##
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39 ## @seealso{filter, filter2}
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40 ## @end deftypefn
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41
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42 function y = fftfilt (b, x, n)
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43
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44 ## If N is not specified explicitly, we do not use the overlap-add
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45 ## method at all because loops are really slow. Otherwise, we only
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46 ## ensure that the number of points in the FFT is the smallest power
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47 ## of two larger than N and length(b). This could result in length
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48 ## one blocks, but if the user knows better ...
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49
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50 if (nargin < 2)
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51 print_usage ();
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52 endif
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53
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54 transpose = (rows (x) == 1);
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55
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56 if (transpose)
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57 x = x.';
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58 endif
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59
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60 [r_x, c_x] = size (x);
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61 [r_b, c_b] = size (b);
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62
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63 if (! isvector (b))
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64 error ("fftfilt: B must be a vector");
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65 endif
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66
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67 if (ndims (x) != 2)
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68 error ("fftfilt: X must be a 1-D or 2-D array");
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69 endif
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70
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71 l_b = r_b * c_b;
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72 b = reshape (b, l_b, 1);
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73
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74 if (nargin == 2)
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75 ## Use FFT with the smallest power of 2 which is >= length (x) +
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76 ## length (b) - 1 as number of points ...
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77 n = 2 ^ nextpow2 (r_x + l_b - 1);
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78 B = fft (b, n);
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79 y = ifft (fft (x, n) .* B(:, ones (1, c_x)));
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80 else
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81 ## Use overlap-add method ...
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82 if (! (isscalar (n)))
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83 error ("fftfilt: N has to be a scalar");
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84 endif
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85 n = 2 ^ nextpow2 (max ([n, l_b]));
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86 L = n - l_b + 1;
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87 B = fft (b, n);
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88 B = B(:, ones (c_x,1));
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89 R = ceil (r_x / L);
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90 y = zeros (r_x, c_x);
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91 for r = 1:R
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92 lo = (r - 1) * L + 1;
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93 hi = min (r * L, r_x);
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94 tmp = zeros (n, c_x);
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95 tmp(1:(hi-lo+1),:) = x(lo:hi,:);
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96 tmp = ifft (fft (tmp) .* B);
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97 hi = min (lo+n-1, r_x);
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98 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:);
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99 endfor
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100 endif
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101
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102 y = y(1:r_x, :);
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103
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104 ## Final cleanups:
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105
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106 ## - If both b and x are real, y should be real.
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107 ## - If b is real and x is imaginary, y should be imaginary.
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108 ## - If b is imaginary and x is real, y should be imaginary.
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109 ## - If both b and x are imaginary, y should be real.
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110 xisreal = all (imag (x) == 0);
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111 xisimag = all (real (x) == 0);
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112
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113 if (all (imag (b) == 0))
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114 y (:,xisreal) = real (y (:,xisreal));
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115 y (:,xisimag) = complex (real (y (:,xisimag)) * 0, imag (y (:,xisimag)));
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116 elseif (all (real (b) == 0))
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117 y (:,xisreal) = complex (real (y (:,xisreal)) * 0, imag (y (:,xisreal)));
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118 y (:,xisimag) = real (y (:,xisimag));
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119 endif
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120
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121 ## - If both x and b are integer in both real and imaginary
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122 ## components, y should be integer.
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123 if (! any (b - fix (b)))
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124 idx = find (! any (x - fix (x)));
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125 y (:, idx) = round (y (:, idx));
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126 endif
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127
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128 ## Transpose after cleanup, otherwise rounding fails.
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129 if (transpose)
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130 y = y.';
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131 endif
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132
c5d35bb139b6 [project @ 1994-10-11 00:34:13 by jwe]
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133 endfunction
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134
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135
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136 %!shared b, x, r
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137
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138 %!testif HAVE_FFTW
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139 %! b = [1 1];
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140 %! x = [1, zeros(1,9)];
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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 ), [1 1 0 0 0 0 0 0 0 0] );
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144 %! assert (fftfilt (b.',x.'), [1 1 0 0 0 0 0 0 0 0].');
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145 %! assert (fftfilt (b, [x.' x.']), [1 1 0 0 0 0 0 0 0 0].'*[1 1]);
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146 %! assert (fftfilt (b, [x.'+2*eps x.']) == [1 1 0 0 0 0 0 0 0 0].'*[1 1],
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147 %! [false(10, 1) true(10, 1)]);
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148
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149 %!testif HAVE_FFTW
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150 %! r = sqrt (1/2) * (1+i);
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151 %! b = b*r;
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152 %! assert (fftfilt (b, x ), r*[1 1 0 0 0 0 0 0 0 0] , eps );
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153 %! assert (fftfilt (b, r*x), r*r*[1 1 0 0 0 0 0 0 0 0], 2*eps);
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154 %! assert (fftfilt (b, x.'), r*[1 1 0 0 0 0 0 0 0 0].', eps );
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155
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156 %!testif HAVE_FFTW
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157 %! b = [1 1];
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158 %! x = zeros (10,3); x(1,1)=-1; x(1,2)=1;
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159 %! y0 = zeros (10,3); y0(1:2,1)=-1; y0(1:2,2)=1;
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160 %! y = fftfilt (b, x);
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161 %! assert (y0, y);
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162 %! y = fftfilt (b*i, x);
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163 %! assert (y0*i, y);
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164 %! y = fftfilt (b, x*i);
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165 %! assert (y0*i, y);
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166 %! y = fftfilt (b*i, x*i);
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167 %! assert (-y0, y);
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168 %! x = rand (10, 1);
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169 %! y = fftfilt (b, [x x*i]);
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170 %! assert (true, isreal (y(:,1)));
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171 %! assert (false, any (real (y(:,2))));
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172
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173 %!testif HAVE_FFTW
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174 %! b = rand (10, 1);
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175 %! x = rand (10, 1);
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176 %! y0 = filter (b, 1, x);
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177 %! y = fftfilt (b, x);
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178 %! assert (y0, y, 16*eps);
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179 %! y0 = filter (b*i, 1, x*i);
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180 %! y = fftfilt (b*i, x*i);
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181 %! assert (y0, y, 16*eps);
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182
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183 %!testif HAVE_FFTW
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184 %! b = rand (10, 1) + i*rand (10, 1);
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185 %! x = rand (10, 1) + i*rand (10, 1);
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186 %! y0 = filter (b, 1, x);
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187 %! y = fftfilt (b, x);
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188 %! assert (y0, y, 55*eps);
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189
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190 ## Test input validation
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191 %!error <Invalid call> fftfilt (1)
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192 %!error fftfilt (ones (2), 1)
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193 %!error fftfilt (2, ones (3,3,3))
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194 %!error fftfilt (2, 1, ones (2))