FFT(3) User Contributed Perl Documentation FFT(3)NAMEPDL::FFT - FFTs for PDL
DESCRIPTION
!!!!!!!!!!!!!!!!!!!!!!!!!!WARNING!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
As of PDL-2.006_04, the direction of the FFT/IFFT has been reversed to
match the usage in the FFTW library and the convention in use
generally.
!!!!!!!!!!!!!!!!!!!!!!!!!!WARNING!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
FFTs for PDL. These work for arrays of any dimension, although ones
with small prime factors are likely to be the quickest. The forward
FFT is unnormalized while the inverse FFT is normalized so that the
IFFT of the FFT returns the original values.
For historical reasons, these routines work in-place and do not
recognize the in-place flag. That should be fixed.
SYNOPSIS
use PDL::FFT qw/:Func/;
fft($real, $imag);
ifft($real, $imag);
realfft($real);
realifft($real);
fftnd($real,$imag);
ifftnd($real,$imag);
$kernel = kernctr($image,$smallk);
fftconvolve($image,$kernel);
DATA TYPES
The underlying C library upon which this module is based performs FFTs
on both single precision and double precision floating point piddles.
Performing FFTs on integer data types is not reliable. Consider the
following FFT on piddles of type 'double':
$r = pdl(0,1,0,1);
$i = zeroes($r);
fft($r,$i);
print $r,$i;
[2 0 -2 0] [0 0 0 0]
But if $r and $i are unsigned short integers (ushorts):
$r = pdl(ushort,0,1,0,1);
$i = zeroes($r);
fft($r,$i);
print $r,$i;
[2 0 65534 0] [0 0 0 0]
This used to occur because PDL::PP converts the ushort piddles to
floats or doubles, performs the FFT on them, and then converts them
back to ushort, causing the overflow where the amplitude of the
frequency should be -2.
Therefore, if you pass in a piddle of integer datatype (byte, short,
ushort, long) to any of the routines in PDL::FFT, your data will be
promoted to a double-precision piddle. If you pass in a float, the
single-precision FFT will be performed.
FREQUENCIES
For even-sized input arrays, the frequencies are packed like normal for
FFTs (where N is the size of the array and D is the physical step size
between elements):
0, 1/ND, 2/ND, ..., (N/2-1)/ND, 1/2D, -(N/2-1)/ND, ..., -1/ND.
which can easily be obtained (taking the Nyquist frequency to be
positive) using
"$kx = $real->xlinvals(-($N/2-1)/$N/$D,1/2/$D)->rotate(-($N/2 -1));"
For odd-sized input arrays the Nyquist frequency is not directly
acessible, and the frequencies are
0, 1/ND, 2/ND, ..., (N/2-0.5)/ND, -(N/2-0.5)/ND, ..., -1/ND.
which can easily be obtained using
"$kx =
$real->xlinvals(-($N/2-0.5)/$N/$D,($N/2-0.5)/$N/$D)->rotate(-($N-1)/2);"
ALTERNATIVE FFT PACKAGES
Various other modules - such as PDL::FFTW and PDL::Slatec - contain FFT
routines. However, unlike PDL::FFT, these modules are optional, and so
may not be installed.
FUNCTIONSfft()
Complex 1-D FFT of the "real" and "imag" arrays [inplace].
Signature: ([o,nc]real(n); [o,nc]imag(n))
fft($real,$imag);
ifft()
Complex inverse 1-D FFT of the "real" and "imag" arrays [inplace].
Signature: ([o,nc]real(n); [o,nc]imag(n))
ifft($real,$imag);
realfft()
One-dimensional FFT of real function [inplace].
The real part of the transform ends up in the first half of the array
and the imaginary part of the transform ends up in the second half of
the array.
realfft($real);
realifft()
Inverse of one-dimensional realfft routine [inplace].
realifft($real);
fftnd()
N-dimensional FFT over all pdl dims of input (inplace)
fftnd($real,$imag);
ifftnd()
N-dimensional inverse FFT over all pdl dims of input (inplace)
ifftnd($real,$imag);
fftconvolve()
N-dimensional convolution with periodic boundaries (FFT method)
$kernel = kernctr($image,$smallk);
fftconvolve($image,$kernel);
fftconvolve works inplace, and returns an error array in kernel as an
accuracy check -- all the values in it should be negligible.
See also PDL::ImageND::convolveND, which performs speed-optimized
convolution with a variety of boundary conditions.
The sizes of the image and the kernel must be the same. kernctr
centres a small kernel to emulate the behaviour of the direct
convolution routines.
The speed cross-over between using straight convolution
(PDL::Image2D::conv2d()) and these fft routines is for kernel sizes
roughly 7x7.
convmath
Signature: ([o,nc]a(m); [o,nc]b(m))
Internal routine doing maths for convolution
convmath does not process bad values. It will set the bad-value flag
of all output piddles if the flag is set for any of the input piddles.
cmul
Signature: (ar(); ai(); br(); bi(); [o]cr(); [o]ci())
Complex multiplication
cmul does not process bad values. It will set the bad-value flag of
all output piddles if the flag is set for any of the input piddles.
cdiv
Signature: (ar(); ai(); br(); bi(); [o]cr(); [o]ci())
Complex division
cdiv does not process bad values. It will set the bad-value flag of
all output piddles if the flag is set for any of the input piddles.
BUGS
Where the source is marked `FIX', could re-implement using phase-shift
factors on the transforms and some real-space bookkeeping, to save some
temporary space and redundant transforms.
AUTHOR
This file copyright (C) 1997, 1998 R.J.R. Williams
(rjrw@ast.leeds.ac.uk), Karl Glazebrook (kgb@aaoepp.aao.gov.au), Tuomas
J. Lukka, (lukka@husc.harvard.edu). All rights reserved. There is no
warranty. You are allowed to redistribute this software / documentation
under certain conditions. For details, see the file COPYING in the PDL
distribution. If this file is separated from the PDL distribution, the
copyright notice should be included in the file.
perl v5.18.1 2014-01-17 FFT(3)
