FFTW(3)

NAME
PDL::FFTW - PDL interface to the Fastest Fourier Transform in the West v2.x

DESCRIPTION
This is a means to interface PDL with the FFTW library. It's similar to the standard FFT routine but it's usually faster and has support for real transforms. It works well for the types of PDLs for which was the library was compiled (otherwise it must do conversions).

SYNOPSIS
    use PDL::FFTW

    load_wisdom("file_name");

    out_cplx_pdl =  fftw(in_cplx_pdl);
    out_cplx_pdl = ifftw(in_cplx_pdl);

    out_cplx_pdl =  rfftw(in_real_pdl);
    out_real_pdl = irfftw(in_cplx_pdl);

    cplx_pdl = nfftw(cplx_pdl);
    cplx_pdl = infftw(cplx_pdl);

    cplx_pdl = Cmul(a_cplx_pdl, b_cplx_pdl);
    cplx_pdl = Cconj(a_cplx_pdl);
    real_pdl = Cmod(a_cplx_pdl);
    real_pdl = Cmod2(a_cplx_pdl);

FFTW documentation
Please refer to the FFTW documentation for a better understanding of these functions.

Note that complex numbers are represented as piddles with leading dimension size 2 (real/imaginary pairs).

FUNCTIONS

  load_wisdom
Loads the wisdom from a file for better FFTW performance.

The wisdom is automatically saved when the program ends. It will be automagically called when the variable $PDL::FFT::wisdom is set to a file name. For example, the following is a useful idiom to have in your .perldlrc file:

  $PDL::FFT::wisdom = "$ENV{HOME}/.fftwisdom"; # save fftw wisdom in this file

Explicit usage:

  load_wisdom($fname);

  fftw
calculate the complex FFT of a real piddle (complex input, complex output)

   $pdl_cplx = fftw $pdl_cplx;

  ifftw
Complex inverse FFT (complex input, complex output).

   $pdl_cplx = ifftw $pdl_cplx;

  nfftw
Complex inplace FFT (complex input, complex output).

   $pdl_cplx = nfftw $pdl_cplx;

  infftw
Complex inplace inverse FFT (complex input, complex output).

   $pdl_cplx = infftw $pdl_cplx;

  rfftw
Real FFT. For an input piddle of dimensions [n1,n2,...] the output is [2,(n1/2)+1,n2,...] (real input, complex output).

  $pdl_cplx = fftw $pdl_real;

  irfftw
Real inverse FFT. Have a look at rfftw to understand the format. USE ONLY an even n1! (complex input, real output)

  $pdl_real = ifftw $pdl_cplx;

  nrfftw
Real inplace FFT. If you want a transformation on a piddle with dimensions [n1,n2,....] you MUST pass in a piddle with dimensions [2*(n1/2+1),n2,...] (real input, complex output).

Use with care due to dimension restrictions mentioned below. For details check the html docs that come with the fftw library.

  $pdl_cplx = nrfftw $pdl_real;

  inrfftw
Real inplace inverse FFT. Have a look at nrfftw to understand the format. USE ONLY an even first dimension size! (complex input, real output)

  $pdl_real = infftw $pdl_cplx;

  rfftwconv
ND convolution using real ffts from the FFTW library

  $conv = rfftwconv $im, kernctr $im, $k; # kernctr is from PDL::FFT

  fftwconv
ND convolution using complex ffts from the FFTW library

Assumes real input!

  $conv = fftwconv $im, kernctr $im, $k; # kernctr is from PDL::FFT

  Cmul
  Signature: (a(n); b(n); [o]c(n))

Complex multiplication

   $out_pdl_cplx = Cmul($a_pdl_cplx,$b_pdl_cplx);

  Cscale
  Signature: (a(n); b(); [o]c(n))

Complex by real multiplation.

  Cscale($a_pdl_cplx,$b_pdl_real);

  Cdiv
  Signature: (a(n); b(n); [o]c(n))

Complex division.

  $out_pdl_cplx = Cdiv($a_pdl_cplx,$b_pdl_cplx);

  Cbmul
  Signature: (a(n); b(n))

Complex inplace multiplication.

   Cbmul($a_pdl_cplx,$b_pdl_cplx);

  Cbscale
  Signature: (a(n); b())

Complex inplace multiplaction by real.

   Cbscale($a_pdl_cplx,$b_pdl_real);

  Cconj
  Signature: (a(n); [o]c(n))

Complex conjugate.

   $out_pdl_cplx = Cconj($a_pdl_cplx);

  Cbconj
  Signature: (a(n))

Complex inplace conjugate.

   Cbconj($a_pdl_cplx);

  Cexp
  Signature: (a(n); [o]c(n))

Complex exponentation.

   $out_pdl_cplx = Cexp($a_pdl_cplx);

  Cbexp
  Signature: (a(n))

Complex inplace exponentation.

   $out_pdl_cplx = Cexp($a_pdl_cplx);

  Cmod
  Signature: (a(n); [o]c())

modulus of a complex piddle.

  $out_pdl_real = Cmod($a_pdl_cplx);

  Carg
  Signature: (a(n); [o]c())

argument of a complex number.

   $out_pdl_real = Carg($a_pdl_cplx);

  Cmod2
  Signature: (a(n); [o]c())

Returns squared modulus of a complex number.

   $out_pdl_real = Cmod2($a_pdl_cplx);

AUTHOR
Copyright (C) 1999 Christian Pellegrin, 2000 Christian Soeller. 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.