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<title>GNU Scientific Library – Reference Manual: DWT Initialization</title>
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<a name="DWT-Initialization"></a>
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<p>
Next: <a href="DWT-Transform-Functions.html#DWT-Transform-Functions" accesskey="n" rel="next">DWT Transform Functions</a>, Previous: <a href="DWT-Definitions.html#DWT-Definitions" accesskey="p" rel="previous">DWT Definitions</a>, Up: <a href="Wavelet-Transforms.html#Wavelet-Transforms" accesskey="u" rel="up">Wavelet Transforms</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Initialization"></a>
<h3 class="section">31.2 Initialization</h3>
<a name="index-DWT-initialization"></a>
<a name="index-gsl_005fwavelet_005ftype"></a>
<p>The <code>gsl_wavelet</code> structure contains the filter coefficients
defining the wavelet and any associated offset parameters.
</p>
<dl>
<dt><a name="index-gsl_005fwavelet_005falloc"></a>Function: <em>gsl_wavelet *</em> <strong>gsl_wavelet_alloc</strong> <em>(const gsl_wavelet_type * <var>T</var>, size_t <var>k</var>)</em></dt>
<dd><a name="index-gsl_005fwavelet"></a>
<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></dd></dl>
<p>The following wavelet types are implemented:
</p>
<dl>
<dt><a name="index-gsl_005fwavelet_005fdaubechies"></a>Wavelet: <strong>gsl_wavelet_daubechies</strong></dt>
<dt><a name="index-gsl_005fwavelet_005fdaubechies_005fcentered"></a>Wavelet: <strong>gsl_wavelet_daubechies_centered</strong></dt>
<dd><a name="index-Daubechies-wavelets"></a>
<a name="index-maximal-phase_002c-Daubechies-wavelets"></a>
<p>This is the Daubechies wavelet family of maximum phase with <em>k/2</em>
vanishing moments. The implemented wavelets are
<em>k=4, 6, …, 20</em>, with <var>k</var> even.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fwavelet_005fhaar"></a>Wavelet: <strong>gsl_wavelet_haar</strong></dt>
<dt><a name="index-gsl_005fwavelet_005fhaar_005fcentered"></a>Wavelet: <strong>gsl_wavelet_haar_centered</strong></dt>
<dd><a name="index-Haar-wavelets"></a>
<p>This is the Haar wavelet. The only valid choice of <em>k</em> for the
Haar wavelet is <em>k=2</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fwavelet_005fbspline"></a>Wavelet: <strong>gsl_wavelet_bspline</strong></dt>
<dt><a name="index-gsl_005fwavelet_005fbspline_005fcentered"></a>Wavelet: <strong>gsl_wavelet_bspline_centered</strong></dt>
<dd><a name="index-biorthogonal-wavelets"></a>
<a name="index-B_002dspline-wavelets"></a>
<p>This is the biorthogonal B-spline wavelet family of order <em>(i,j)</em>.
The implemented values of <em>k = 100*i + j</em> are 103, 105, 202, 204,
206, 208, 301, 303, 305 307, 309.
</p></dd></dl>
<p>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.
</p>
<dl>
<dt><a name="index-gsl_005fwavelet_005fname"></a>Function: <em>const char *</em> <strong>gsl_wavelet_name</strong> <em>(const gsl_wavelet * <var>w</var>)</em></dt>
<dd><p>This function returns a pointer to the name of the wavelet family for
<var>w</var>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fwavelet_005ffree"></a>Function: <em>void</em> <strong>gsl_wavelet_free</strong> <em>(gsl_wavelet * <var>w</var>)</em></dt>
<dd><p>This function frees the wavelet object <var>w</var>.
</p></dd></dl>
<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.
</p>
<dl>
<dt><a name="index-gsl_005fwavelet_005fworkspace_005falloc"></a>Function: <em>gsl_wavelet_workspace *</em> <strong>gsl_wavelet_workspace_alloc</strong> <em>(size_t <var>n</var>)</em></dt>
<dd><a name="index-gsl_005fwavelet_005fworkspace"></a>
<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. A null pointer is returned if insufficient memory is available.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fwavelet_005fworkspace_005ffree"></a>Function: <em>void</em> <strong>gsl_wavelet_workspace_free</strong> <em>(gsl_wavelet_workspace * <var>work</var>)</em></dt>
<dd><p>This function frees the allocated workspace <var>work</var>.
</p></dd></dl>
<hr>
<div class="header">
<p>
Next: <a href="DWT-Transform-Functions.html#DWT-Transform-Functions" accesskey="n" rel="next">DWT Transform Functions</a>, Previous: <a href="DWT-Definitions.html#DWT-Definitions" accesskey="p" rel="previous">DWT Definitions</a>, Up: <a href="Wavelet-Transforms.html#Wavelet-Transforms" accesskey="u" rel="up">Wavelet Transforms</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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