NAME

Math::GSL::Wavelet - 1-D (Real) Wavelets

SYNOPSIS

use Math::GSL::Wavelet qw/:all/;

DESCRIPTION

gsl_wavelet_alloc($T, $k)

This function allocates and initializes a wavelet object of type $T, where $T must be one of the constants below. The parameter $k selects the specific member of the wavelet family.

gsl_wavelet_free($w)

This function frees the wavelet object $w.

gsl_wavelet_name

gsl_wavelet_workspace_alloc($n)

This function allocates a workspace for the discrete wavelet transform. To perform a one-dimensional transform on $n elements, a workspace of size $n must be provided. For two-dimensional transforms of $n-by-$n matrices it is sufficient to allocate a workspace of size $n, since the transform operates on individual rows and columns.

gsl_wavelet_workspace_free($work)

This function frees the allocated workspace work.

gsl_wavelet_transform

gsl_wavelet_transform_forward($w, $data, $stride, $n, $work)

This functions compute in-place forward discrete wavelet transforms of length $n with stride $stride on the array $data. The length of the transform $n is restricted to powers of two. For the forward transform, the elements of the original array are replaced by the discrete wavelet transform f_i -> w_{j,k} in a packed triangular storage layout, where j is the index of the level j = 0 ... J-1 and k is the index of the coefficient within each level, k = 0 ... (2^j)-1. The total number of levels is J = \log_2(n). The output data has the following form,

(s_{-1,0}, d_{0,0}, d_{1,0}, d_{1,1}, d_{2,0}, ..., d_{j,k}, ..., d_{J-1,2^{J-1}-1})

where the first element is the smoothing coefficient s_{-1,0}, followed by the detail coefficients d_{j,k} for each level j. The backward transform inverts these coefficients to obtain the original data. These functions return a status of $GSL_SUCCESS upon successful completion. $GSL_EINVAL is returned if $n is not an integer power of 2 or if insufficient workspace is provided.

gsl_wavelet_transform_inverse

This module also contains the following constants with their valid k value for the gsl_wavelet_alloc function :

$gsl_wavelet_daubechies

$gsl_wavelet_daubechies_centered

This is the Daubechies wavelet family of maximum phase with k/2 vanishing moments. The implemented wavelets are k=4, 6, ..., 20, with k even.

$gsl_wavelet_haar

$gsl_wavelet_haar_centered

This is the Haar wavelet. The only valid choice of k for the Haar wavelet is k=2.

$gsl_wavelet_bspline

$gsl_wavelet_bspline_centered

This is the biorthogonal B-spline wavelet family of order (i,j). The implemented values of k = 100*i + j are 103, 105, 202, 204, 206, 208, 301, 303, 305 307, 309.

AUTHORS

Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>

COPYRIGHT AND LICENSE

Copyright (C) 2008-2021 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.