Mercurial > octave
annotate scripts/signal/fftfilt.m @ 29359:7854d5752dd2
maint: merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 10 Feb 2021 10:10:40 -0500 |
parents | d8318c12d903 0a5b15007766 |
children | 01de0045b2e3 |
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/>. |
2313 | 7 ## |
8 ## This file is part of Octave. | |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
2313 | 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. |
2313 | 14 ## |
15 ## Octave is distributed in the hope that it will be useful, but | |
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. |
2313 | 19 ## |
20 ## You should have received a copy of the GNU General Public License | |
7016 | 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 ######################################################################## |
1026 | 25 |
3367 | 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. |
3426 | 30 ## |
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31 ## If @var{x} is a matrix, filter each column of the matrix. |
3426 | 32 ## |
3367 | 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. |
3890 | 38 ## |
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39 ## @seealso{filter, filter2} |
3367 | 40 ## @end deftypefn |
2312 | 41 |
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42 function y = fftfilt (b, x, n) |
787 | 43 |
2325 | 44 ## If N is not specified explicitly, we do not use the overlap-add |
2303 | 45 ## method at all because loops are really slow. Otherwise, we only |
46 ## ensure that the number of points in the FFT is the smallest power | |
47 ## of two larger than N and length(b). This could result in length | |
48 ## one blocks, but if the user knows better ... | |
2325 | 49 |
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50 if (nargin < 2) |
6046 | 51 print_usage (); |
787 | 52 endif |
2325 | 53 |
3890 | 54 transpose = (rows (x) == 1); |
55 | |
56 if (transpose) | |
57 x = x.'; | |
58 endif | |
59 | |
787 | 60 [r_x, c_x] = size (x); |
61 [r_b, c_b] = size (b); | |
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"); |
787 | 69 endif |
2325 | 70 |
3890 | 71 l_b = r_b * c_b; |
72 b = reshape (b, l_b, 1); | |
2325 | 73 |
787 | 74 if (nargin == 2) |
2303 | 75 ## Use FFT with the smallest power of 2 which is >= length (x) + |
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))); |
787 | 80 else |
2303 | 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"); |
787 | 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)); |
3890 | 89 R = ceil (r_x / L); |
90 y = zeros (r_x, c_x); | |
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91 for r = 1:R |
3890 | 92 lo = (r - 1) * L + 1; |
93 hi = min (r * L, r_x); | |
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94 tmp = zeros (n, c_x); |
3890 | 95 tmp(1:(hi-lo+1),:) = x(lo:hi,:); |
96 tmp = ifft (fft (tmp) .* B); | |
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97 hi = min (lo+n-1, r_x); |
3890 | 98 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:); |
2325 | 99 endfor |
787 | 100 endif |
2325 | 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)); |
3890 | 119 endif |
787 | 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 |
1026 | 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.'; |
787 | 131 endif |
132 | |
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 |
25586 | 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], [false(10, 1) true(10, 1)]); |
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147 |
25586 | 148 %!testif HAVE_FFTW |
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149 %! r = sqrt (1/2) * (1+i); |
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150 %! b = b*r; |
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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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152 %! assert (fftfilt (b, r*x), r*r*[1 1 0 0 0 0 0 0 0 0], 2*eps); |
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153 %! assert (fftfilt (b, x.'), r*[1 1 0 0 0 0 0 0 0 0].', eps ); |
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154 |
25586 | 155 %!testif HAVE_FFTW |
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156 %! b = [1 1]; |
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157 %! x = zeros (10,3); x(1,1)=-1; x(1,2)=1; |
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158 %! y0 = zeros (10,3); y0(1:2,1)=-1; y0(1:2,2)=1; |
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159 %! y = fftfilt (b, x); |
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160 %! assert (y0, y); |
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161 %! y = fftfilt (b*i, x); |
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162 %! assert (y0*i, y); |
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163 %! y = fftfilt (b, x*i); |
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164 %! assert (y0*i, y); |
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165 %! y = fftfilt (b*i, x*i); |
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166 %! assert (-y0, y); |
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167 %! x = rand (10, 1); |
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168 %! y = fftfilt (b, [x x*i]); |
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169 %! assert (true, isreal (y(:,1))); |
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170 %! assert (false, any (real (y(:,2)))); |
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171 |
25586 | 172 %!testif HAVE_FFTW |
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173 %! b = rand (10, 1); |
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174 %! x = rand (10, 1); |
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175 %! y0 = filter (b, 1, x); |
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176 %! y = fftfilt (b, x); |
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177 %! assert (y0, y, 16*eps); |
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178 %! y0 = filter (b*i, 1, x*i); |
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179 %! y = fftfilt (b*i, x*i); |
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180 %! assert (y0, y, 16*eps); |
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181 |
25586 | 182 %!testif HAVE_FFTW |
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183 %! b = rand (10, 1) + i*rand (10, 1); |
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184 %! x = rand (10, 1) + i*rand (10, 1); |
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185 %! y0 = filter (b, 1, x); |
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186 %! y = fftfilt (b, x); |
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187 %! assert (y0, y, 55*eps); |
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188 |
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189 ## Test input validation |
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190 %!error <Invalid call> fftfilt (1) |
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191 %!error fftfilt (ones (2), 1) |
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192 %!error fftfilt (2, ones (3,3,3)) |
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193 %!error fftfilt (2, 1, ones (2)) |