Mercurial > hg > octave-nkf
annotate scripts/signal/fftfilt.m @ 20788:7374a3a6d594
use new string_value method to handle value extraction errors
* urlwrite.cc: Use new string_value method.
author | John W. Eaton <jwe@octave.org> |
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date | Thu, 08 Oct 2015 17:26:40 -0400 |
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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}) |
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22 ## Filter @var{x} with the FIR filter @var{b} using the FFT. |
3426 | 23 ## |
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24 ## If @var{x} is a matrix, filter each column of the matrix. |
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 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. |
3890 | 31 ## |
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32 ## @seealso{filter, filter2} |
3367 | 33 ## @end deftypefn |
2312 | 34 |
5428 | 35 ## Author: Kurt Hornik <Kurt.Hornik@wu-wien.ac.at> |
2312 | 36 ## Created: 3 September 1994 |
37 ## Adapted-By: jwe | |
787 | 38 |
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39 function y = fftfilt (b, x, n) |
787 | 40 |
2325 | 41 ## If N is not specified explicitly, we do not use the overlap-add |
2303 | 42 ## method at all because loops are really slow. Otherwise, we only |
43 ## ensure that the number of points in the FFT is the smallest power | |
44 ## of two larger than N and length(b). This could result in length | |
45 ## one blocks, but if the user knows better ... | |
2325 | 46 |
787 | 47 if (nargin < 2 || nargin > 3) |
6046 | 48 print_usage (); |
787 | 49 endif |
2325 | 50 |
3890 | 51 transpose = (rows (x) == 1); |
52 | |
53 if (transpose) | |
54 x = x.'; | |
55 endif | |
56 | |
787 | 57 [r_x, c_x] = size (x); |
58 [r_b, c_b] = size (b); | |
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"); |
787 | 66 endif |
2325 | 67 |
3890 | 68 l_b = r_b * c_b; |
69 b = reshape (b, l_b, 1); | |
2325 | 70 |
787 | 71 if (nargin == 2) |
2303 | 72 ## Use FFT with the smallest power of 2 which is >= length (x) + |
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))); |
787 | 77 else |
2303 | 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"); |
787 | 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)); |
3890 | 86 R = ceil (r_x / L); |
87 y = zeros (r_x, c_x); | |
1026 | 88 for r = 1:R; |
3890 | 89 lo = (r - 1) * L + 1; |
90 hi = min (r * L, r_x); | |
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91 tmp = zeros (n, c_x); |
3890 | 92 tmp(1:(hi-lo+1),:) = x(lo:hi,:); |
93 tmp = ifft (fft (tmp) .* B); | |
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94 hi = min (lo+n-1, r_x); |
3890 | 95 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:); |
2325 | 96 endfor |
787 | 97 endif |
2325 | 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)); |
3890 | 116 endif |
787 | 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 |
1026 | 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.'; |
787 | 128 endif |
129 | |
130 endfunction | |
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131 |
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132 |
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133 %!shared b, x, r |
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134 |
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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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144 |
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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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151 |
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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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168 |
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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 |