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);

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.

Cscale

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

Complex by real multiplation.

  Cscale($a_pdl_cplx,$b_pdl_real);

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

Complex division.

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

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.

Cbmul

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

Complex inplace multiplication.

   Cbmul($a_pdl_cplx,$b_pdl_cplx);

Cbmul 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.

Cbscale

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

Complex inplace multiplaction by real.

   Cbscale($a_pdl_cplx,$b_pdl_real);

Cbscale 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.

Cconj

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

Complex conjugate.

   $out_pdl_cplx = Cconj($a_pdl_cplx);

Cconj 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.

Cbconj

  Signature: (a(n))

Complex inplace conjugate.

   Cbconj($a_pdl_cplx);

Cbconj 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.

Cexp

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

Complex exponentation.

   $out_pdl_cplx = Cexp($a_pdl_cplx);

Cexp 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.

Cbexp

  Signature: (a(n))

Complex inplace exponentation.

   $out_pdl_cplx = Cexp($a_pdl_cplx);

Cbexp 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.

Cmod

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

modulus of a complex piddle.

  $out_pdl_real = Cmod($a_pdl_cplx);

Cmod 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.

Carg

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

argument of a complex number.

   $out_pdl_real = Carg($a_pdl_cplx);

Carg 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.

Cmod2

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

Returns squared modulus of a complex number.

   $out_pdl_real = Cmod2($a_pdl_cplx);

Cmod2 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.

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.