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<title>DWT Initialization - GNU Scientific Library -- Reference Manual</title>
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<a name="DWT-Initialization"></a>
Next: <a rel="next" accesskey="n" href="DWT-Transform-Functions.html">DWT Transform Functions</a>,
Previous: <a rel="previous" accesskey="p" href="DWT-Definitions.html">DWT Definitions</a>,
Up: <a rel="up" accesskey="u" href="Wavelet-Transforms.html">Wavelet Transforms</a>
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<h3 class="section">30.2 Initialization</h3>
<p><a name="index-DWT-initialization-2155"></a>
The <code>gsl_wavelet</code> structure contains the filter coefficients
defining the wavelet and any associated offset parameters.
<div class="defun">
— Function: gsl_wavelet * <b>gsl_wavelet_alloc</b> (<var>const gsl_wavelet_type * T, size_t k</var>)<var><a name="index-gsl_005fwavelet_005falloc-2156"></a></var><br>
<blockquote><p>This function allocates and initializes a wavelet object of type
<var>T</var>. The parameter <var>k</var> selects the specific member of the
wavelet family. A null pointer is returned if insufficient memory is
available or if a unsupported member is selected.
</p></blockquote></div>
<p>The following wavelet types are implemented:
<div class="defun">
— Wavelet: <b>gsl_wavelet_daubechies</b><var><a name="index-gsl_005fwavelet_005fdaubechies-2157"></a></var><br>
— Wavelet: <b>gsl_wavelet_daubechies_centered</b><var><a name="index-gsl_005fwavelet_005fdaubechies_005fcentered-2158"></a></var><br>
<blockquote><p><a name="index-Daubechies-wavelets-2159"></a><a name="index-maximal-phase_002c-Daubechies-wavelets-2160"></a>The is the Daubechies wavelet family of maximum phase with k/2
vanishing moments. The implemented wavelets are
<!-- {$k=4, 6, \dots, 20$} -->
k=4, 6, <small class="dots">...</small>, 20, with <var>k</var> even.
</p></blockquote></div>
<div class="defun">
— Wavelet: <b>gsl_wavelet_haar</b><var><a name="index-gsl_005fwavelet_005fhaar-2161"></a></var><br>
— Wavelet: <b>gsl_wavelet_haar_centered</b><var><a name="index-gsl_005fwavelet_005fhaar_005fcentered-2162"></a></var><br>
<blockquote><p><a name="index-Haar-wavelets-2163"></a>This is the Haar wavelet. The only valid choice of k for the
Haar wavelet is k=2.
</p></blockquote></div>
<div class="defun">
— Wavelet: <b>gsl_wavelet_bspline</b><var><a name="index-gsl_005fwavelet_005fbspline-2164"></a></var><br>
— Wavelet: <b>gsl_wavelet_bspline_centered</b><var><a name="index-gsl_005fwavelet_005fbspline_005fcentered-2165"></a></var><br>
<blockquote><p><a name="index-biorthogonal-wavelets-2166"></a><a name="index-B_002dspline-wavelets-2167"></a>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.
</p></blockquote></div>
<p class="noindent">The centered forms of the wavelets align the coefficients of the various
sub-bands on edges. Thus the resulting visualization of the
coefficients of the wavelet transform in the phase plane is easier to
understand.
<div class="defun">
— Function: const char * <b>gsl_wavelet_name</b> (<var>const gsl_wavelet * w</var>)<var><a name="index-gsl_005fwavelet_005fname-2168"></a></var><br>
<blockquote><p>This function returns a pointer to the name of the wavelet family for
<var>w</var>.
</p></blockquote></div>
<!-- @deftypefun {void} gsl_wavelet_print (const gsl_wavelet * @var{w}) -->
<!-- This function prints the filter coefficients (@code{**h1}, @code{**g1}, @code{**h2}, @code{**g2}) of the wavelet object @var{w}. -->
<!-- @end deftypefun -->
<div class="defun">
— Function: void <b>gsl_wavelet_free</b> (<var>gsl_wavelet * w</var>)<var><a name="index-gsl_005fwavelet_005ffree-2169"></a></var><br>
<blockquote><p>This function frees the wavelet object <var>w</var>.
</p></blockquote></div>
<p>The <code>gsl_wavelet_workspace</code> structure contains scratch space of the
same size as the input data and is used to hold intermediate results
during the transform.
<div class="defun">
— Function: gsl_wavelet_workspace * <b>gsl_wavelet_workspace_alloc</b> (<var>size_t n</var>)<var><a name="index-gsl_005fwavelet_005fworkspace_005falloc-2170"></a></var><br>
<blockquote><p>This function allocates a workspace for the discrete wavelet transform.
To perform a one-dimensional transform on <var>n</var> elements, a workspace
of size <var>n</var> must be provided. For two-dimensional transforms of
<var>n</var>-by-<var>n</var> matrices it is sufficient to allocate a workspace of
size <var>n</var>, since the transform operates on individual rows and
columns.
</p></blockquote></div>
<div class="defun">
— Function: void <b>gsl_wavelet_workspace_free</b> (<var>gsl_wavelet_workspace * work</var>)<var><a name="index-gsl_005fwavelet_005fworkspace_005ffree-2171"></a></var><br>
<blockquote><p>This function frees the allocated workspace <var>work</var>.
</p></blockquote></div>
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