1FFT(3)                User Contributed Perl Documentation               FFT(3)
2
3
4

NAME

6       PDL::FFT - FFTs for PDL
7

DESCRIPTION

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
15       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
20       For historical reasons, these routines work in-place and do not
21       recognize the in-place flag.  That should be fixed.
22

SYNOPSIS

24               use PDL::FFT qw/:Func/;
25
26               fft($real, $imag);
27               ifft($real, $imag);
28               realfft($real);
29               realifft($real);
30
31               fftnd($real,$imag);
32               ifftnd($real,$imag);
33
34               $kernel = kernctr($image,$smallk);
35               fftconvolve($image,$kernel);
36

DATA TYPES

38       The underlying C library upon which this module is based performs FFTs
39       on both single precision and double precision floating point piddles.
40       Performing FFTs on integer data types is not reliable.  Consider the
41       following FFT on piddles of type 'double':
42
43               $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
49       But if $r and $i are unsigned short integers (ushorts):
50
51               $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
57       This used to occur because PDL::PP converts the ushort piddles 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
62       Therefore, if you pass in a piddle 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 piddle.  If you pass in a float, the
65       single-precision FFT will be performed.
66

FREQUENCIES

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
72        0, 1/ND, 2/ND, ..., (N/2-1)/ND, 1/2D, -(N/2-1)/ND, ..., -1/ND.
73
74       which can easily be obtained (taking the Nyquist frequency to be
75       positive) using
76
77       "$kx = $real->xlinvals(-($N/2-1)/$N/$D,1/2/$D)->rotate(-($N/2 -1));"
78
79       For odd-sized input arrays the Nyquist frequency is not directly
80       acessible, and the frequencies are
81
82        0, 1/ND, 2/ND, ..., (N/2-0.5)/ND, -(N/2-0.5)/ND, ..., -1/ND.
83
84       which can easily be obtained using
85
86       "$kx =
87       $real->xlinvals(-($N/2-0.5)/$N/$D,($N/2-0.5)/$N/$D)->rotate(-($N-1)/2);"
88

ALTERNATIVE FFT PACKAGES

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

FUNCTIONS

95   fft()
96       Complex 1-D FFT of the "real" and "imag" arrays [inplace].
97
98         Signature: ([o,nc]real(n); [o,nc]imag(n))
99
100       fft($real,$imag);
101
102   ifft()
103       Complex inverse 1-D FFT of the "real" and "imag" arrays [inplace].
104
105         Signature: ([o,nc]real(n); [o,nc]imag(n))
106
107       ifft($real,$imag);
108
109   realfft()
110       One-dimensional FFT of real function [inplace].
111
112       The real part of the transform ends up in the first half of the array
113       and the imaginary part of the transform ends up in the second half of
114       the array.
115
116               realfft($real);
117
118   realifft()
119       Inverse of one-dimensional realfft routine [inplace].
120
121               realifft($real);
122
123   fftnd()
124       N-dimensional FFT over all pdl dims of input (inplace)
125
126               fftnd($real,$imag);
127
128   ifftnd()
129       N-dimensional inverse FFT over all pdl dims of input (inplace)
130
131               ifftnd($real,$imag);
132
133   fftconvolve()
134       N-dimensional convolution with periodic boundaries (FFT method)
135
136               $kernel = kernctr($image,$smallk);
137               fftconvolve($image,$kernel);
138
139       fftconvolve works inplace, and returns an error array in kernel as an
140       accuracy check -- all the values in it should be negligible.
141
142       See also PDL::ImageND::convolveND, which performs speed-optimized
143       convolution with a variety of boundary conditions.
144
145       The sizes of the image and the kernel must be the same.  kernctr
146       centres a small kernel to emulate the behaviour of the direct
147       convolution routines.
148
149       The speed cross-over between using straight convolution
150       (PDL::Image2D::conv2d()) and these fft routines is for kernel sizes
151       roughly 7x7.
152
153   convmath
154         Signature: ([o,nc]a(m); [o,nc]b(m))
155
156       Internal routine doing maths for convolution
157
158       convmath does not process bad values.  It will set the bad-value flag
159       of all output piddles if the flag is set for any of the input piddles.
160
161   cmul
162         Signature: (ar(); ai(); br(); bi(); [o]cr(); [o]ci())
163
164       Complex multiplication
165
166       cmul does not process bad values.  It will set the bad-value flag of
167       all output piddles if the flag is set for any of the input piddles.
168
169   cdiv
170         Signature: (ar(); ai(); br(); bi(); [o]cr(); [o]ci())
171
172       Complex division
173
174       cdiv does not process bad values.  It will set the bad-value flag of
175       all output piddles if the flag is set for any of the input piddles.
176

BUGS

178       Where the source is marked `FIX', could re-implement using phase-shift
179       factors on the transforms and some real-space bookkeeping, to save some
180       temporary space and redundant transforms.
181

AUTHOR

183       This file copyright (C) 1997, 1998 R.J.R. Williams
184       (rjrw@ast.leeds.ac.uk), Karl Glazebrook (kgb@aaoepp.aao.gov.au), Tuomas
185       J. Lukka, (lukka@husc.harvard.edu).  All rights reserved. There is no
186       warranty. You are allowed to redistribute this software / documentation
187       under certain conditions. For details, see the file COPYING in the PDL
188       distribution. If this file is separated from the PDL distribution, the
189       copyright notice should be included in the file.
190
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193perl v5.28.0                      2018-07-23                            FFT(3)
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