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,$kernel);
36
38 The underlying C library upon which this module is based performs FFTs
39 on both single precision and double precision floating point ndarrays.
40 The PP functions are defined to only take those data types. Therefore,
41 if you pass in an ndarray of integer datatype (byte, short, ushort,
42 long) to any of the routines in PDL::FFT, your data will be promoted to
43 a double-precision ndarray. If you pass in a float, the single-
44 precision FFT will be performed.
45
47 For even-sized input arrays, the frequencies are packed like normal for
48 FFTs (where N is the size of the array and D is the physical step size
49 between elements):
50 0, 1/ND, 2/ND, ..., (N/2-1)/ND, 1/2D, -(N/2-1)/ND, ..., -1/ND.
52 which can easily be obtained (taking the Nyquist frequency to be
54 positive) using
55 "$kx = $real->xlinvals(-($N/2-1)/$N/$D,1/2/$D)->rotate(-($N/2 -1));"
57 For odd-sized input arrays the Nyquist frequency is not directly
59 acessible, and the frequencies are
60 0, 1/ND, 2/ND, ..., (N/2-0.5)/ND, -(N/2-0.5)/ND, ..., -1/ND.
62 which can easily be obtained using
64 "$kx =
66 $real->xlinvals(-($N/2-0.5)/$N/$D,($N/2-0.5)/$N/$D)->rotate(-($N-1)/2);"
67
69 Various other modules - such as PDL::FFTW3 and PDL::Slatec - contain
70 FFT routines. However, unlike PDL::FFT, these modules are optional,
71 and so may not be installed.
72
74 fft
75 Signature: ([io]real(n); [io]imag(n))
76 Complex 1-D FFT of the "real" and "imag" arrays [inplace]. A single
78 cfloat/cdouble input ndarray can also be used.
79 fft($real,$imag);
81 fft($complex);
82 fft does not process bad values. It will set the bad-value flag of all
84 output ndarrays if the flag is set for any of the input ndarrays.
85 ifft
87 Signature: ([io]real(n); [io]imag(n))
88 Complex inverse 1-D FFT of the "real" and "imag" arrays [inplace]. A
90 single cfloat/cdouble input ndarray can also be used.
91 ifft($real,$imag);
93 ifft($complex);
94 ifft does not process bad values. It will set the bad-value flag of
96 all output ndarrays if the flag is set for any of the input ndarrays.
97 realfft()
99 One-dimensional FFT of real function [inplace].
100 The real part of the transform ends up in the first half of the array
102 and the imaginary part of the transform ends up in the second half of
103 the array.
104 realfft($real);
106 realifft()
108 Inverse of one-dimensional realfft routine [inplace].
109 realifft($real);
111 fftnd()
113 N-dimensional FFT over all pdl dims of input (inplace)
114 fftnd($real,$imag);
116 ifftnd()
118 N-dimensional inverse FFT over all pdl dims of input (inplace)
119 ifftnd($real,$imag);
121 fftconvolve()
123 N-dimensional convolution with periodic boundaries (FFT method)
124 $kernel = kernctr($image,$smallk);
126 fftconvolve($image,$kernel);
127 fftconvolve works inplace, and returns an error array in kernel as an
129 accuracy check -- all the values in it should be negligible.
130 See also PDL::ImageND::convolveND, which performs speed-optimized
132 convolution with a variety of boundary conditions.
133 The sizes of the image and the kernel must be the same. kernctr
135 centres a small kernel to emulate the behaviour of the direct
136 convolution routines.
137 The speed cross-over between using straight convolution
139 (PDL::Image2D::conv2d()) and these fft routines is for kernel sizes
140 roughly 7x7.
141
143 Where the source is marked `FIX', could re-implement using phase-shift
144 factors on the transforms and some real-space bookkeeping, to save some
145 temporary space and redundant transforms.
146
148 This file copyright (C) 1997, 1998 R.J.R. Williams
149 (rjrw@ast.leeds.ac.uk), Karl Glazebrook (kgb@aaoepp.aao.gov.au), Tuomas
150 J. Lukka, (lukka@husc.harvard.edu). All rights reserved. There is no
151 warranty. You are allowed to redistribute this software / documentation
152 under certain conditions. For details, see the file COPYING in the PDL
153 distribution. If this file is separated from the PDL distribution, the
154 copyright notice should be included in the file.
155perl v5.34.0 2022-02-28 FFT(3)