FFT(3) User Contributed Perl Documentation FFT(3)NAMEPDL::FFT - FFTs for PDL
DESCRIPTION
FFTs for PDL. These work for arrays of any dimension, although ones
with small prime factors are likely to be the quickest.
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,$kernel);
ALTERNATIVE FFT PACKAGES
Various other modules - such as PDL::FFTW and PDL::Slatec - contain FFT
routines. However, unlike PDL::FFT, these modules are optional, and so
may not be installed.
FUNCTIONS
fft
Signature: ([o,nc]real(n); [o,nc]imag(n))
Complex FFT of the "real" and "imag" arrays [inplace]
ifft
Signature: ([o,nc]real(n); [o,nc]imag(n))
Complex Inverse FFT of the "real" and "imag" arrays [inplace]
realfft()
One-dimensional FFT of real function [inplace].
The real part of the transform ends up in the first half of the array
and the imaginary part of the transform ends up in the second half of
the array.
realfft($real);
realifft()
Inverse of one-dimensional realfft routine [inplace].
realifft($real);
fftnd()
N-dimensional FFT (inplace)
fftnd($real,$imag);
ifftnd()
N-dimensional inverse FFT
ifftnd($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
cmul
Signature: (ar(); ai(); br(); bi(); [o]cr(); [o]ci())
Complex multiplication
cdiv
Signature: (ar(); ai(); br(); bi(); [o]cr(); [o]ci())
Complex division
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.
POD ERRORS
Hey! The above document had some coding errors, which are explained
below:
Around line 337:
=cut found outside a pod block. Skipping to next block.
perl v5.10.0 2008-08-29 FFT(3)