Mercurial > hg > octave-lyh
annotate scripts/signal/fftfilt.m @ 17173:bb60b1bb47cf
view.m: Fix args undefined error when calling with two arguments
author | Max Brister <max@2bass.com> |
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date | Sat, 03 Aug 2013 17:23:44 -0600 |
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1 ## Copyright (C) 1994-2012 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 -*- |
20 ## @deftypefn {Function File} {} fftfilt (@var{b}, @var{x}, @var{n}) | |
3426 | 21 ## |
3367 | 22 ## With two arguments, @code{fftfilt} filters @var{x} with the FIR filter |
23 ## @var{b} using the FFT. | |
3426 | 24 ## |
3367 | 25 ## Given the optional third argument, @var{n}, @code{fftfilt} uses the |
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26 ## overlap-add method to filter @var{x} with @var{b} using an @var{n}-point |
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27 ## FFT. The FFT size must be an even power of 2 and must be greater than |
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28 ## or equal to the length of @var{b}. If the specified @var{n} does not |
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29 ## meet these criteria, it is automatically adjusted to the nearest value |
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30 ## that does. |
3890 | 31 ## |
32 ## If @var{x} is a matrix, filter each column of the matrix. | |
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33 ## @seealso{filter, filter2} |
3367 | 34 ## @end deftypefn |
2312 | 35 |
5428 | 36 ## Author: Kurt Hornik <Kurt.Hornik@wu-wien.ac.at> |
2312 | 37 ## Created: 3 September 1994 |
38 ## Adapted-By: jwe | |
787 | 39 |
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40 function y = fftfilt (b, x, n) |
787 | 41 |
2325 | 42 ## If N is not specified explicitly, we do not use the overlap-add |
2303 | 43 ## method at all because loops are really slow. Otherwise, we only |
44 ## ensure that the number of points in the FFT is the smallest power | |
45 ## of two larger than N and length(b). This could result in length | |
46 ## one blocks, but if the user knows better ... | |
2325 | 47 |
787 | 48 if (nargin < 2 || nargin > 3) |
6046 | 49 print_usage (); |
787 | 50 endif |
2325 | 51 |
3890 | 52 transpose = (rows (x) == 1); |
53 | |
54 if (transpose) | |
55 x = x.'; | |
56 endif | |
57 | |
787 | 58 [r_x, c_x] = size (x); |
59 [r_b, c_b] = size (b); | |
60 | |
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61 if (! isvector (b)) |
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62 error ("fftfilt: B must be a vector"); |
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63 endif |
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64 |
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65 if (ndims (x) != 2) |
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66 error ("fftfilt: X must be a 1-D or 2-D array"); |
787 | 67 endif |
2325 | 68 |
3890 | 69 l_b = r_b * c_b; |
70 b = reshape (b, l_b, 1); | |
2325 | 71 |
787 | 72 if (nargin == 2) |
2303 | 73 ## Use FFT with the smallest power of 2 which is >= length (x) + |
74 ## length (b) - 1 as number of points ... | |
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75 n = 2 ^ nextpow2 (r_x + l_b - 1); |
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76 B = fft (b, n); |
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77 y = ifft (fft (x, n) .* B(:, ones (1, c_x))); |
787 | 78 else |
2303 | 79 ## Use overlap-add method ... |
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80 if (! (isscalar (n))) |
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81 error ("fftfilt: N has to be a scalar"); |
787 | 82 endif |
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83 n = 2 ^ nextpow2 (max ([n, l_b])); |
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84 L = n - l_b + 1; |
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85 B = fft (b, n); |
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86 B = B(:, ones (c_x,1)); |
3890 | 87 R = ceil (r_x / L); |
88 y = zeros (r_x, c_x); | |
1026 | 89 for r = 1:R; |
3890 | 90 lo = (r - 1) * L + 1; |
91 hi = min (r * L, r_x); | |
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92 tmp = zeros (n, c_x); |
3890 | 93 tmp(1:(hi-lo+1),:) = x(lo:hi,:); |
94 tmp = ifft (fft (tmp) .* B); | |
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95 hi = min (lo+n-1, r_x); |
3890 | 96 y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:); |
2325 | 97 endfor |
787 | 98 endif |
2325 | 99 |
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100 y = y(1:r_x, :); |
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101 |
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102 ## Final cleanups: |
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103 |
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104 ## - If both b and x are real, y should be real. |
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105 ## - If b is real and x is imaginary, y should be imaginary. |
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106 ## - If b is imaginary and x is real, y should be imaginary. |
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107 ## - If both b and x are imaginary, y should be real. |
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108 xisreal = all (imag (x) == 0); |
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109 xisimag = all (real (x) == 0); |
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110 |
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111 if (all (imag (b) == 0)) |
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112 y (:,xisreal) = real (y (:,xisreal)); |
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113 y (:,xisimag) = complex (real (y (:,xisimag)) * 0, imag (y (:,xisimag))); |
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114 elseif (all (real (b) == 0)) |
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115 y (:,xisreal) = complex (real (y (:,xisreal)) * 0, imag (y (:,xisreal))); |
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116 y (:,xisimag) = real (y (:,xisimag)); |
3890 | 117 endif |
787 | 118 |
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119 ## - If both x and b are integer in both real and imaginary |
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120 ## components, y should be integer. |
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121 if (! any (b - fix (b))) |
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122 idx = find (! any (x - fix (x))); |
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123 y (:, idx) = round (y (:, idx)); |
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124 endif |
1026 | 125 |
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126 ## Transpose after cleanup, otherwise rounding fails. |
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127 if (transpose) |
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128 y = y.'; |
787 | 129 endif |
130 | |
131 endfunction | |
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132 |
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133 |
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134 %!shared b, x, r |
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135 |
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136 %!test |
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137 %! b = [1 1]; |
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138 %! x = [1, zeros(1,9)]; |
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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.'), [1 1 0 0 0 0 0 0 0 0].'); |
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143 %! assert (fftfilt (b, [x.' x.']), [1 1 0 0 0 0 0 0 0 0].'*[1 1]); |
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144 %! 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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145 |
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146 %!test |
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147 %! r = sqrt (1/2) * (1+i); |
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148 %! b = b*r; |
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149 %! assert (fftfilt (b, x ), r*[1 1 0 0 0 0 0 0 0 0] , eps ); |
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150 %! assert (fftfilt (b, r*x), r*r*[1 1 0 0 0 0 0 0 0 0], 2*eps); |
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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 |
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153 %!test |
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154 %! b = [1 1]; |
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155 %! x = zeros (10,3); x(1,1)=-1; x(1,2)=1; |
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156 %! y0 = zeros (10,3); y0(1:2,1)=-1; y0(1:2,2)=1; |
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157 %! y = fftfilt (b, x); |
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158 %! assert (y0, y); |
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159 %! y = fftfilt (b*i, x); |
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160 %! assert (y0*i, y); |
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161 %! y = fftfilt (b, x*i); |
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162 %! assert (y0*i, y); |
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163 %! y = fftfilt (b*i, x*i); |
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164 %! assert (-y0, y); |
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165 %! x = rand (10, 1); |
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166 %! y = fftfilt (b, [x x*i]); |
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167 %! assert (true, isreal (y(:,1))); |
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168 %! assert (false, any (real (y(:,2)))); |
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169 |
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170 %!test |
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171 %! b = rand (10, 1); |
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172 %! x = rand (10, 1); |
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173 %! y0 = filter (b, 1, x); |
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174 %! y = fftfilt (b, x); |
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175 %! assert (y0, y, 16*eps); |
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176 %! y0 = filter (b*i, 1, x*i); |
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177 %! y = fftfilt (b*i, x*i); |
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178 %! assert (y0, y, 16*eps); |
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179 |
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180 %!test |
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181 %! b = rand (10, 1) + i*rand (10, 1); |
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182 %! x = rand (10, 1) + i*rand (10, 1); |
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183 %! y0 = filter (b, 1, x); |
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184 %! y = fftfilt (b, x); |
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185 %! assert (y0, y, 55*eps); |
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186 |
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187 %% Test input validation |
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188 %!error fftfilt (1) |
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189 %!error fftfilt (1, 2, 3, 4) |
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190 %!error fftfilt (ones (2), 1) |
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191 %!error fftfilt (2, ones (3,3,3)) |
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192 %!error fftfilt (2, 1, ones (2)) |
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193 |