PDL::FFT - FFTs for PDL

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.

        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);

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.

  Signature: ([o,nc]real(n); [o,nc]imag(n))

Complex FFT of the real and imag arrays [inplace]

fft 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.

  Signature: ([o,nc]real(n); [o,nc]imag(n))

Complex Inverse FFT of the real and imag arrays [inplace]

ifft 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.

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);

Inverse of one-dimensional realfft routine [inplace].

        realifft($real);

N-dimensional FFT (inplace)

        fftnd($real,$imag);

N-dimensional inverse FFT

        ifftnd($real,$imag);

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.

  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.

  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.

  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.

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.

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.