1FFT(3) User Contributed Perl Documentation FFT(3)
2
6 PDL::FFT - FFTs for PDL
7
9 !!!!!!!!!!!!!!!!!!!!!!!!!!WARNING!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
10 As of PDL-2.006_04, the direction of the FFT/IFFT has been reversed to
11 match the usage in the FFTW library and the convention in use
12 generally.
13 !!!!!!!!!!!!!!!!!!!!!!!!!!WARNING!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
14 FFTs for PDL. These work for arrays of any dimension, although ones
16 with small prime factors are likely to be the quickest. The forward
17 FFT is unnormalized while the inverse FFT is normalized so that the
18 IFFT of the FFT returns the original values.
19 For historical reasons, these routines work in-place and do not
21 recognize the in-place flag. That should be fixed.
22
24 use PDL::FFT qw/:Func/;
25 fft($real, $imag);
27 ifft($real, $imag);
28 realfft($real);
29 realifft($real);
30 fftnd($real,$imag);
32 ifftnd($real,$imag);
33 $kernel = kernctr($image,$smallk);
35 fftconvolve($image,$kernel);
36
38 The underlying C library upon which this module is based performs FFTs
39 on both single precision and double precision floating point ndarrays.
40 Performing FFTs on integer data types is not reliable. Consider the
41 following FFT on ndarrays of type 'double':
42 $r = pdl(0,1,0,1);
44 $i = zeroes($r);
45 fft($r,$i);
46 print $r,$i;
47 [2 0 -2 0] [0 0 0 0]
48 But if $r and $i are unsigned short integers (ushorts):
50 $r = pdl(ushort,0,1,0,1);
52 $i = zeroes($r);
53 fft($r,$i);
54 print $r,$i;
55 [2 0 65534 0] [0 0 0 0]
56 This used to occur because PDL::PP converts the ushort ndarrays to
58 floats or doubles, performs the FFT on them, and then converts them
59 back to ushort, causing the overflow where the amplitude of the
60 frequency should be -2.
61 Therefore, if you pass in an ndarray of integer datatype (byte, short,
63 ushort, long) to any of the routines in PDL::FFT, your data will be
64 promoted to a double-precision ndarray. If you pass in a float, the
65 single-precision FFT will be performed.
66
68 For even-sized input arrays, the frequencies are packed like normal for
69 FFTs (where N is the size of the array and D is the physical step size
70 between elements):
71 0, 1/ND, 2/ND, ..., (N/2-1)/ND, 1/2D, -(N/2-1)/ND, ..., -1/ND.
73 which can easily be obtained (taking the Nyquist frequency to be
75 positive) using
76 "$kx = $real->xlinvals(-($N/2-1)/$N/$D,1/2/$D)->rotate(-($N/2 -1));"
78 For odd-sized input arrays the Nyquist frequency is not directly
80 acessible, and the frequencies are
81 0, 1/ND, 2/ND, ..., (N/2-0.5)/ND, -(N/2-0.5)/ND, ..., -1/ND.
83 which can easily be obtained using
85 "$kx =
87 $real->xlinvals(-($N/2-0.5)/$N/$D,($N/2-0.5)/$N/$D)->rotate(-($N-1)/2);"
88
90 Various other modules - such as PDL::FFTW and PDL::Slatec - contain FFT
91 routines. However, unlike PDL::FFT, these modules are optional, and so
92 may not be installed.
93
95 fft()
96 Complex 1-D FFT of the "real" and "imag" arrays [inplace]. A single
97 cfloat/cdouble input ndarray can also be used.
98 Signature: ([o,nc]real(n); [o,nc]imag(n))
100 fft($real,$imag);
102 ifft()
104 Complex inverse 1-D FFT of the "real" and "imag" arrays [inplace]. A
105 single cfloat/cdouble input ndarray can also be used.
106 Signature: ([o,nc]real(n); [o,nc]imag(n))
108 ifft($real,$imag);
110 realfft()
112 One-dimensional FFT of real function [inplace].
113 The real part of the transform ends up in the first half of the array
115 and the imaginary part of the transform ends up in the second half of
116 the array.
117 realfft($real);
119 realifft()
121 Inverse of one-dimensional realfft routine [inplace].
122 realifft($real);
124 fftnd()
126 N-dimensional FFT over all pdl dims of input (inplace)
127 fftnd($real,$imag);
129 ifftnd()
131 N-dimensional inverse FFT over all pdl dims of input (inplace)
132 ifftnd($real,$imag);
134 fftconvolve()
136 N-dimensional convolution with periodic boundaries (FFT method)
137 $kernel = kernctr($image,$smallk);
139 fftconvolve($image,$kernel);
140 fftconvolve works inplace, and returns an error array in kernel as an
142 accuracy check -- all the values in it should be negligible.
143 See also PDL::ImageND::convolveND, which performs speed-optimized
145 convolution with a variety of boundary conditions.
146 The sizes of the image and the kernel must be the same. kernctr
148 centres a small kernel to emulate the behaviour of the direct
149 convolution routines.
150 The speed cross-over between using straight convolution
152 (PDL::Image2D::conv2d()) and these fft routines is for kernel sizes
153 roughly 7x7.
154 convmath
156 Signature: ([o,nc]a(m); [o,nc]b(m))
157 Internal routine doing maths for convolution
159 convmath does not process bad values. It will set the bad-value flag
161 of all output ndarrays if the flag is set for any of the input
162 ndarrays.
163 cmul
165 Signature: (ar(); ai(); br(); bi(); [o]cr(); [o]ci())
166 Complex multiplication
168 cmul does not process bad values. It will set the bad-value flag of
170 all output ndarrays if the flag is set for any of the input ndarrays.
171 cdiv
173 Signature: (ar(); ai(); br(); bi(); [o]cr(); [o]ci())
174 Complex division
176 cdiv does not process bad values. It will set the bad-value flag of
178 all output ndarrays if the flag is set for any of the input ndarrays.
179
181 Where the source is marked `FIX', could re-implement using phase-shift
182 factors on the transforms and some real-space bookkeeping, to save some
183 temporary space and redundant transforms.
184
186 This file copyright (C) 1997, 1998 R.J.R. Williams
187 (rjrw@ast.leeds.ac.uk), Karl Glazebrook (kgb@aaoepp.aao.gov.au), Tuomas
188 J. Lukka, (lukka@husc.harvard.edu). All rights reserved. There is no
189 warranty. You are allowed to redistribute this software / documentation
190 under certain conditions. For details, see the file COPYING in the PDL
191 distribution. If this file is separated from the PDL distribution, the
192 copyright notice should be included in the file.
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