Provided by: libmath-gsl-perl_0.44-1build3_amd64 
NAME
Math::GSL::FFT - Fast Fourier Transforms (FFT)
SYNOPSIS
use Math::GSL::FFT qw /:all/;
my $input1 = [ 0 .. 7 ];
my $N1 = @$input1;
my ($status1, $output1) = gsl_fft_real_radix2_transform ($input, 1, $N1);
my ($status2, $output2) = gsl_fft_halfcomplex_radix2_inverse($output2, 1, $N1);
# $input1 == $output2
my $input2 = [ 0 .. 6 ];
my $N2 = @$input;
my $workspace1 = gsl_fft_real_workspace_alloc($N2);
my $wavetable1 = gsl_fft_real_wavetable_alloc($N2);
my ($status3,$output3) = gsl_fft_real_transform ($input, 1, $N2, $wavetable1, $workspace1);
my $wavetable4 = gsl_fft_halfcomplex_wavetable_alloc($N2);
my $workspace4 = gsl_fft_real_workspace_alloc($N2);
my ($status4,$output4) = gsl_fft_halfcomplex_inverse($output, 1, $N2, $wavetable4, $workspace4);
# $input2 == $output4
DESCRIPTION
• "gsl_fft_complex_radix2_forward($data, $stride, $n) "
This function computes the forward FFTs of length $n with stride $stride, on the array
reference $data using an in-place radix-2 decimation-in-time algorithm. The length of
the transform $n is restricted to powers of two. For the transform version of the
function the sign argument can be either forward (-1) or backward (+1). The functions
return a value of $GSL_SUCCESS if no errors were detected, or $GSL_EDOM if the length
of the data $n is not a power of two.
• "gsl_fft_complex_radix2_backward "
• "gsl_fft_complex_radix2_inverse "
• "gsl_fft_complex_radix2_transform "
• "gsl_fft_complex_radix2_dif_forward "
• "gsl_fft_complex_radix2_dif_backward "
• "gsl_fft_complex_radix2_dif_inverse "
• "gsl_fft_complex_radix2_dif_transform "
• gsl_fft_complex_wavetable_alloc($n)
This function prepares a trigonometric lookup table for a complex FFT of length $n.
The function returns a pointer to the newly allocated gsl_fft_complex_wavetable if no
errors were detected, and a null pointer in the case of error. The length $n is
factorized into a product of subtransforms, and the factors and their trigonometric
coefficients are stored in the wavetable. The trigonometric coefficients are computed
using direct calls to sin and cos, for accuracy. Recursion relations could be used to
compute the lookup table faster, but if an application performs many FFTs of the same
length then this computation is a one-off overhead which does not affect the final
throughput. The wavetable structure can be used repeatedly for any transform of the
same length. The table is not modified by calls to any of the other FFT functions.
The same wavetable can be used for both forward and backward (or inverse) transforms
of a given length.
• gsl_fft_complex_wavetable_free($wavetable)
This function frees the memory associated with the wavetable $wavetable. The wavetable
can be freed if no further FFTs of the same length will be needed.
• gsl_fft_complex_workspace_alloc($n)
This function allocates a workspace for a complex transform of length $n.
• gsl_fft_complex_workspace_free($workspace)
This function frees the memory associated with the workspace $workspace. The workspace
can be freed if no further FFTs of the same length will be needed.
• "gsl_fft_complex_memcpy "
• "gsl_fft_complex_forward "
• "gsl_fft_complex_backward "
• "gsl_fft_complex_inverse "
• "gsl_fft_complex_transform "
• "gsl_fft_halfcomplex_radix2_backward($data, $stride, $n)"
This function computes the backwards in-place radix-2 FFT of length $n and stride
$stride on the half-complex sequence data stored according the output scheme used by
gsl_fft_real_radix2. The result is a real array stored in natural order.
• "gsl_fft_halfcomplex_radix2_inverse($data, $stride, $n)"
This function computes the inverse in-place radix-2 FFT of length $n and stride
$stride on the half-complex sequence data stored according the output scheme used by
gsl_fft_real_radix2. The result is a real array stored in natural order.
• "gsl_fft_halfcomplex_radix2_transform"
• gsl_fft_halfcomplex_wavetable_alloc($n)
This function prepares trigonometric lookup tables for an FFT of size $n real
elements. The functions return a pointer to the newly allocated struct if no errors
were detected, and a null pointer in the case of error. The length $n is factorized
into a product of subtransforms, and the factors and their trigonometric coefficients
are stored in the wavetable. The trigonometric coefficients are computed using direct
calls to sin and cos, for accuracy. Recursion relations could be used to compute the
lookup table faster, but if an application performs many FFTs of the same length then
computing the wavetable is a one-off overhead which does not affect the final
throughput. The wavetable structure can be used repeatedly for any transform of the
same length. The table is not modified by calls to any of the other FFT functions.
The appropriate type of wavetable must be used for forward real or inverse half-
complex transforms.
• gsl_fft_halfcomplex_wavetable_free($wavetable)
This function frees the memory associated with the wavetable $wavetable. The wavetable
can be freed if no further FFTs of the same length will be needed.
• "gsl_fft_halfcomplex_backward "
• "gsl_fft_halfcomplex_inverse "
• "gsl_fft_halfcomplex_transform "
• "gsl_fft_halfcomplex_unpack "
• "gsl_fft_halfcomplex_radix2_unpack "
• "gsl_fft_real_radix2_transform($data, $stride, $n) "
This function computes an in-place radix-2 FFT of length $n and stride $stride on the
real array reference $data. The output is a half-complex sequence, which is stored in-
place. The arrangement of the half-complex terms uses the following scheme: for k <
N/2 the real part of the k-th term is stored in location k, and the corresponding
imaginary part is stored in location N-k. Terms with k > N/2 can be reconstructed
using the symmetry z_k = z^*_{N-k}. The terms for k=0 and k=N/2 are both purely real,
and count as a special case. Their real parts are stored in locations 0 and N/2
respectively, while their imaginary parts which are zero are not stored. The following
table shows the correspondence between the output data and the equivalent results
obtained by considering the input data as a complex sequence with zero imaginary part,
complex[0].real = data[0]
complex[0].imag = 0
complex[1].real = data[1]
complex[1].imag = data[N-1]
............... ................
complex[k].real = data[k]
complex[k].imag = data[N-k]
............... ................
complex[N/2].real = data[N/2]
complex[N/2].imag = 0
............... ................
complex[k'].real = data[k] k' = N - k
complex[k'].imag = -data[N-k]
............... ................
complex[N-1].real = data[1]
complex[N-1].imag = -data[N-1]
Note that the output data can be converted into the full complex sequence using the
function gsl_fft_halfcomplex_unpack.
• gsl_fft_real_wavetable_alloc($n)
This function prepares trigonometric lookup tables for an FFT of size $n real
elements. The functions return a pointer to the newly allocated struct if no errors
were detected, and a null pointer in the case of error. The length $n is factorized
into a product of subtransforms, and the factors and their trigonometric coefficients
are stored in the wavetable. The trigonometric coefficients are computed using direct
calls to sin and cos, for accuracy. Recursion relations could be used to compute the
lookup table faster, but if an application performs many FFTs of the same length then
computing the wavetable is a one-off overhead which does not affect the final
throughput. The wavetable structure can be used repeatedly for any transform of the
same length. The table is not modified by calls to any of the other FFT functions.
The appropriate type of wavetable must be used for forward real or inverse half-
complex transforms.
• gsl_fft_real_wavetable_free($wavetable)
This function frees the memory associated with the wavetable $wavetable. The wavetable
can be freed if no further FFTs of the same length will be needed.
• gsl_fft_real_workspace_alloc($n)
This function allocates a workspace for a real transform of length $n. The same
workspace can be used for both forward real and inverse halfcomplex transforms.
• gsl_fft_real_workspace_free($workspace)
This function frees the memory associated with the workspace $workspace. The workspace
can be freed if no further FFTs of the same length will be needed.
• "gsl_fft_real_transform "
• "gsl_fft_real_unpack "
This module also includes the following constants :
• $gsl_fft_forward
• $gsl_fft_backward
For more information on the functions, we refer you to the GSL official documentation:
<http://www.gnu.org/software/gsl/manual/html_node/>
AUTHORS
Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
COPYRIGHT AND LICENSE
Copyright (C) 2008-2023 Jonathan "Duke" Leto and Thierry Moisan
This program is free software; you can redistribute it and/or modify it under the same
terms as Perl itself.