Mercurial > octave
annotate scripts/signal/fftfilt.m @ 27923:bd51beb6205e
update formatting of copyright notices
* Use <https://octave.org/copyright/> instead of
<https://octave.org/COPYRIGHT.html/>.
* For consistency with other comments in the Octave sources, use
C++-style comments for copyright blocks in C and C++ files.
* Use delimiters above and below copyright blocks that are appropriate
for the language used in the file.
* Eliminate extra spacing inside copyright blocks.
* lex.ll (looks_like_copyright): Also allow newlines and carriage
returns before the word "Copyright".
* scripts/mk-doc.pl (gethelp): Also skip empty comment lines.
* bp-table.cc, type.m: Adjust tests.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 08 Jan 2020 11:59:41 -0500 |
parents | 1891570abac8 |
children | bdad8ca48700 |
rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 1994-2020 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 |
5428 | 42 ## Author: Kurt Hornik <Kurt.Hornik@wu-wien.ac.at> |
2312 | 43 ## Created: 3 September 1994 |
44 ## Adapted-By: jwe | |
787 | 45 |
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46 function y = fftfilt (b, x, n) |
787 | 47 |
2325 | 48 ## If N is not specified explicitly, we do not use the overlap-add |
2303 | 49 ## method at all because loops are really slow. Otherwise, we only |
50 ## ensure that the number of points in the FFT is the smallest power | |
51 ## of two larger than N and length(b). This could result in length | |
52 ## one blocks, but if the user knows better ... | |
2325 | 53 |
787 | 54 if (nargin < 2 || nargin > 3) |
6046 | 55 print_usage (); |
787 | 56 endif |
2325 | 57 |
3890 | 58 transpose = (rows (x) == 1); |
59 | |
60 if (transpose) | |
61 x = x.'; | |
62 endif | |
63 | |
787 | 64 [r_x, c_x] = size (x); |
65 [r_b, c_b] = size (b); | |
66 | |
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67 if (! isvector (b)) |
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68 error ("fftfilt: B must be a vector"); |
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69 endif |
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70 |
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71 if (ndims (x) != 2) |
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72 error ("fftfilt: X must be a 1-D or 2-D array"); |
787 | 73 endif |
2325 | 74 |
3890 | 75 l_b = r_b * c_b; |
76 b = reshape (b, l_b, 1); | |
2325 | 77 |
787 | 78 if (nargin == 2) |
2303 | 79 ## Use FFT with the smallest power of 2 which is >= length (x) + |
80 ## length (b) - 1 as number of points ... | |
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81 n = 2 ^ nextpow2 (r_x + l_b - 1); |
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82 B = fft (b, n); |
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83 y = ifft (fft (x, n) .* B(:, ones (1, c_x))); |
787 | 84 else |
2303 | 85 ## Use overlap-add method ... |
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86 if (! (isscalar (n))) |
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87 error ("fftfilt: N has to be a scalar"); |
787 | 88 endif |
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89 n = 2 ^ nextpow2 (max ([n, l_b])); |
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90 L = n - l_b + 1; |
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91 B = fft (b, n); |
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92 B = B(:, ones (c_x,1)); |
3890 | 93 R = ceil (r_x / L); |
94 y = zeros (r_x, c_x); | |
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95 for r = 1:R |
3890 | 96 lo = (r - 1) * L + 1; |
97 hi = min (r * L, r_x); | |
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98 tmp = zeros (n, c_x); |
3890 | 99 tmp(1:(hi-lo+1),:) = x(lo:hi,:); |
100 tmp = ifft (fft (tmp) .* B); | |
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101 hi = min (lo+n-1, r_x); |
3890 | 102 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:); |
2325 | 103 endfor |
787 | 104 endif |
2325 | 105 |
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106 y = y(1:r_x, :); |
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107 |
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108 ## Final cleanups: |
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109 |
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110 ## - If both b and x are real, y should be real. |
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111 ## - If b is real and x is imaginary, y should be imaginary. |
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112 ## - If b is imaginary and x is real, y should be imaginary. |
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113 ## - If both b and x are imaginary, y should be real. |
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114 xisreal = all (imag (x) == 0); |
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115 xisimag = all (real (x) == 0); |
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116 |
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117 if (all (imag (b) == 0)) |
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118 y (:,xisreal) = real (y (:,xisreal)); |
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119 y (:,xisimag) = complex (real (y (:,xisimag)) * 0, imag (y (:,xisimag))); |
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120 elseif (all (real (b) == 0)) |
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121 y (:,xisreal) = complex (real (y (:,xisreal)) * 0, imag (y (:,xisreal))); |
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122 y (:,xisimag) = real (y (:,xisimag)); |
3890 | 123 endif |
787 | 124 |
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125 ## - If both x and b are integer in both real and imaginary |
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126 ## components, y should be integer. |
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127 if (! any (b - fix (b))) |
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128 idx = find (! any (x - fix (x))); |
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129 y (:, idx) = round (y (:, idx)); |
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130 endif |
1026 | 131 |
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132 ## Transpose after cleanup, otherwise rounding fails. |
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133 if (transpose) |
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134 y = y.'; |
787 | 135 endif |
136 | |
137 endfunction | |
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138 |
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139 |
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140 %!shared b, x, r |
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141 |
25586 | 142 %!testif HAVE_FFTW |
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143 %! b = [1 1]; |
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144 %! x = [1, zeros(1,9)]; |
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145 %! assert (fftfilt (b, x ), [1 1 0 0 0 0 0 0 0 0] ); |
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146 %! assert (fftfilt (b, x.'), [1 1 0 0 0 0 0 0 0 0].'); |
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147 %! assert (fftfilt (b.',x ), [1 1 0 0 0 0 0 0 0 0] ); |
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148 %! assert (fftfilt (b.',x.'), [1 1 0 0 0 0 0 0 0 0].'); |
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149 %! assert (fftfilt (b, [x.' x.']), [1 1 0 0 0 0 0 0 0 0].'*[1 1]); |
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150 %! 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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151 |
25586 | 152 %!testif HAVE_FFTW |
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153 %! r = sqrt (1/2) * (1+i); |
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154 %! b = b*r; |
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155 %! assert (fftfilt (b, x ), r*[1 1 0 0 0 0 0 0 0 0] , eps ); |
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156 %! assert (fftfilt (b, r*x), r*r*[1 1 0 0 0 0 0 0 0 0], 2*eps); |
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157 %! assert (fftfilt (b, x.'), r*[1 1 0 0 0 0 0 0 0 0].', eps ); |
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158 |
25586 | 159 %!testif HAVE_FFTW |
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160 %! b = [1 1]; |
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161 %! x = zeros (10,3); x(1,1)=-1; x(1,2)=1; |
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162 %! y0 = zeros (10,3); y0(1:2,1)=-1; y0(1:2,2)=1; |
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163 %! y = fftfilt (b, x); |
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164 %! assert (y0, y); |
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165 %! y = fftfilt (b*i, x); |
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166 %! assert (y0*i, y); |
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167 %! y = fftfilt (b, x*i); |
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168 %! assert (y0*i, y); |
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169 %! y = fftfilt (b*i, x*i); |
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170 %! assert (-y0, y); |
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171 %! x = rand (10, 1); |
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172 %! y = fftfilt (b, [x x*i]); |
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173 %! assert (true, isreal (y(:,1))); |
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174 %! assert (false, any (real (y(:,2)))); |
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175 |
25586 | 176 %!testif HAVE_FFTW |
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177 %! b = rand (10, 1); |
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178 %! x = rand (10, 1); |
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179 %! y0 = filter (b, 1, x); |
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180 %! y = fftfilt (b, x); |
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181 %! assert (y0, y, 16*eps); |
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182 %! y0 = filter (b*i, 1, x*i); |
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183 %! y = fftfilt (b*i, x*i); |
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184 %! assert (y0, y, 16*eps); |
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185 |
25586 | 186 %!testif HAVE_FFTW |
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187 %! b = rand (10, 1) + i*rand (10, 1); |
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188 %! x = rand (10, 1) + i*rand (10, 1); |
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189 %! y0 = filter (b, 1, x); |
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190 %! y = fftfilt (b, x); |
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191 %! assert (y0, y, 55*eps); |
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192 |
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193 ## Test input validation |
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194 %!error fftfilt (1) |
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195 %!error fftfilt (1, 2, 3, 4) |
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196 %!error fftfilt (ones (2), 1) |
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197 %!error fftfilt (2, ones (3,3,3)) |
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198 %!error fftfilt (2, 1, ones (2)) |