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FFT(3)		      User Contributed Perl Documentation		FFT(3)

NAME
       PDL::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)
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