Chris Marshall > PDL-2.006 > PDL::FFTW

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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).

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

Complex multiplication

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

Cscale

Complex by real multiplation.

  $out_pdl_cplx = Cscale($a_pdl_cplx,$b_pdl_real);

Cdiv

Complex division.

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

Cbmul

Complex inplace multiplication.

   Cbmul($a_pdl_cplx,$b_pdl_cplx);

Cbscale

Complex inplace multiplaction by real.

   Cbscale($a_pdl_cplx,$b_pdl_real);

Cconj

Complex conjugate.

   $out_pdl_cplx = Cconj($a_pdl_cplx);

Cbconj

Complex inplace conjugate.

   Cbconj($a_pdl_cplx);

Cexp

Complex exponentation.

   $out_pdl_cplx = Cexp($a_pdl_cplx);

Cbexp

Complex inplace exponentation.

   $out_pdl_cplx = Cbexp($a_pdl_cplx);

Cmod

modulus of a complex piddle.

  $out_pdl_real = Cmod($a_pdl_cplx);

Carg

argument of a complex number.

   $out_pdl_real = Carg($a_pdl_cplx);

Cmod2

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.

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