Mercurial > octave
annotate scripts/signal/fftfilt.m @ 19697:4197fc428c7d
maint: Update copyright notices for 2015.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 11 Feb 2015 14:19:08 -0500 |
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1 ## Copyright (C) 1994-2015 John W. Eaton |
2313 | 2 ## |
3 ## This file is part of Octave. | |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
6 ## under the terms of the GNU General Public License as published by | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
2313 | 9 ## |
10 ## Octave is distributed in the hope that it will be useful, but | |
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
13 ## General Public License for more details. | |
14 ## | |
15 ## You should have received a copy of the GNU General Public License | |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
1026 | 18 |
3367 | 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}) |
3426 | 22 ## |
3367 | 23 ## With two arguments, @code{fftfilt} filters @var{x} with the FIR filter |
24 ## @var{b} using the FFT. | |
3426 | 25 ## |
3367 | 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 |
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28 ## FFT@. The FFT size must be an even power of 2 and must be greater than |
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29 ## or equal to the length of @var{b}. If the specified @var{n} does not |
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30 ## meet these criteria, it is automatically adjusted to the nearest value |
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31 ## that does. |
3890 | 32 ## |
33 ## If @var{x} is a matrix, filter each column of the matrix. | |
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34 ## @seealso{filter, filter2} |
3367 | 35 ## @end deftypefn |
2312 | 36 |
5428 | 37 ## Author: Kurt Hornik <Kurt.Hornik@wu-wien.ac.at> |
2312 | 38 ## Created: 3 September 1994 |
39 ## Adapted-By: jwe | |
787 | 40 |
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41 function y = fftfilt (b, x, n) |
787 | 42 |
2325 | 43 ## If N is not specified explicitly, we do not use the overlap-add |
2303 | 44 ## method at all because loops are really slow. Otherwise, we only |
45 ## ensure that the number of points in the FFT is the smallest power | |
46 ## of two larger than N and length(b). This could result in length | |
47 ## one blocks, but if the user knows better ... | |
2325 | 48 |
787 | 49 if (nargin < 2 || nargin > 3) |
6046 | 50 print_usage (); |
787 | 51 endif |
2325 | 52 |
3890 | 53 transpose = (rows (x) == 1); |
54 | |
55 if (transpose) | |
56 x = x.'; | |
57 endif | |
58 | |
787 | 59 [r_x, c_x] = size (x); |
60 [r_b, c_b] = size (b); | |
61 | |
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62 if (! isvector (b)) |
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63 error ("fftfilt: B must be a vector"); |
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64 endif |
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65 |
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66 if (ndims (x) != 2) |
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67 error ("fftfilt: X must be a 1-D or 2-D array"); |
787 | 68 endif |
2325 | 69 |
3890 | 70 l_b = r_b * c_b; |
71 b = reshape (b, l_b, 1); | |
2325 | 72 |
787 | 73 if (nargin == 2) |
2303 | 74 ## Use FFT with the smallest power of 2 which is >= length (x) + |
75 ## length (b) - 1 as number of points ... | |
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76 n = 2 ^ nextpow2 (r_x + l_b - 1); |
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77 B = fft (b, n); |
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78 y = ifft (fft (x, n) .* B(:, ones (1, c_x))); |
787 | 79 else |
2303 | 80 ## Use overlap-add method ... |
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81 if (! (isscalar (n))) |
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82 error ("fftfilt: N has to be a scalar"); |
787 | 83 endif |
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84 n = 2 ^ nextpow2 (max ([n, l_b])); |
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85 L = n - l_b + 1; |
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86 B = fft (b, n); |
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87 B = B(:, ones (c_x,1)); |
3890 | 88 R = ceil (r_x / L); |
89 y = zeros (r_x, c_x); | |
1026 | 90 for r = 1:R; |
3890 | 91 lo = (r - 1) * L + 1; |
92 hi = min (r * L, r_x); | |
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93 tmp = zeros (n, c_x); |
3890 | 94 tmp(1:(hi-lo+1),:) = x(lo:hi,:); |
95 tmp = ifft (fft (tmp) .* B); | |
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96 hi = min (lo+n-1, r_x); |
3890 | 97 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:); |
2325 | 98 endfor |
787 | 99 endif |
2325 | 100 |
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101 y = y(1:r_x, :); |
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102 |
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103 ## Final cleanups: |
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104 |
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105 ## - If both b and x are real, y should be real. |
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106 ## - If b is real and x is imaginary, y should be imaginary. |
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107 ## - If b is imaginary and x is real, y should be imaginary. |
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108 ## - If both b and x are imaginary, y should be real. |
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109 xisreal = all (imag (x) == 0); |
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110 xisimag = all (real (x) == 0); |
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111 |
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112 if (all (imag (b) == 0)) |
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113 y (:,xisreal) = real (y (:,xisreal)); |
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114 y (:,xisimag) = complex (real (y (:,xisimag)) * 0, imag (y (:,xisimag))); |
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115 elseif (all (real (b) == 0)) |
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116 y (:,xisreal) = complex (real (y (:,xisreal)) * 0, imag (y (:,xisreal))); |
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117 y (:,xisimag) = real (y (:,xisimag)); |
3890 | 118 endif |
787 | 119 |
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120 ## - If both x and b are integer in both real and imaginary |
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121 ## components, y should be integer. |
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122 if (! any (b - fix (b))) |
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123 idx = find (! any (x - fix (x))); |
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124 y (:, idx) = round (y (:, idx)); |
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125 endif |
1026 | 126 |
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127 ## Transpose after cleanup, otherwise rounding fails. |
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128 if (transpose) |
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129 y = y.'; |
787 | 130 endif |
131 | |
132 endfunction | |
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133 |
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134 |
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135 %!shared b, x, r |
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136 |
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137 %!test |
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138 %! b = [1 1]; |
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139 %! x = [1, zeros(1,9)]; |
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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.'), [1 1 0 0 0 0 0 0 0 0].'); |
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144 %! assert (fftfilt (b, [x.' x.']), [1 1 0 0 0 0 0 0 0 0].'*[1 1]); |
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145 %! 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 |
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147 %!test |
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148 %! r = sqrt (1/2) * (1+i); |
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149 %! b = b*r; |
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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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151 %! assert (fftfilt (b, r*x), r*r*[1 1 0 0 0 0 0 0 0 0], 2*eps); |
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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 |
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154 %!test |
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155 %! b = [1 1]; |
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156 %! x = zeros (10,3); x(1,1)=-1; x(1,2)=1; |
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157 %! y0 = zeros (10,3); y0(1:2,1)=-1; y0(1:2,2)=1; |
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158 %! y = fftfilt (b, x); |
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159 %! assert (y0, y); |
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160 %! y = fftfilt (b*i, x); |
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161 %! assert (y0*i, y); |
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162 %! y = fftfilt (b, x*i); |
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163 %! assert (y0*i, y); |
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164 %! y = fftfilt (b*i, x*i); |
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165 %! assert (-y0, y); |
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166 %! x = rand (10, 1); |
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167 %! y = fftfilt (b, [x x*i]); |
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168 %! assert (true, isreal (y(:,1))); |
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169 %! assert (false, any (real (y(:,2)))); |
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170 |
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171 %!test |
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172 %! b = rand (10, 1); |
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173 %! x = rand (10, 1); |
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174 %! y0 = filter (b, 1, x); |
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175 %! y = fftfilt (b, x); |
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176 %! assert (y0, y, 16*eps); |
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177 %! y0 = filter (b*i, 1, x*i); |
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178 %! y = fftfilt (b*i, x*i); |
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179 %! assert (y0, y, 16*eps); |
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180 |
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181 %!test |
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182 %! b = rand (10, 1) + i*rand (10, 1); |
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183 %! x = rand (10, 1) + i*rand (10, 1); |
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184 %! y0 = filter (b, 1, x); |
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185 %! y = fftfilt (b, x); |
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186 %! assert (y0, y, 55*eps); |
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187 |
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188 %% Test input validation |
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189 %!error fftfilt (1) |
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190 %!error fftfilt (1, 2, 3, 4) |
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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)) |
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194 |