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<title>GNU Scientific Library – Reference Manual: DWT in one dimension</title>
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<a name="DWT-in-one-dimension"></a>
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<p>
Next: <a href="DWT-in-two-dimension.html#DWT-in-two-dimension" accesskey="n" rel="next">DWT in two dimension</a>, Up: <a href="DWT-Transform-Functions.html#DWT-Transform-Functions" accesskey="u" rel="up">DWT Transform Functions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Wavelet-transforms-in-one-dimension"></a>
<h4 class="subsection">32.3.1 Wavelet transforms in one dimension</h4>
<a name="index-DWT_002c-one-dimensional"></a>
<dl>
<dt><a name="index-gsl_005fwavelet_005ftransform"></a>Function: <em>int</em> <strong>gsl_wavelet_transform</strong> <em>(const gsl_wavelet * <var>w</var>, double * <var>data</var>, size_t <var>stride</var>, size_t <var>n</var>, gsl_wavelet_direction <var>dir</var>, gsl_wavelet_workspace * <var>work</var>)</em></dt>
<dt><a name="index-gsl_005fwavelet_005ftransform_005fforward"></a>Function: <em>int</em> <strong>gsl_wavelet_transform_forward</strong> <em>(const gsl_wavelet * <var>w</var>, double * <var>data</var>, size_t <var>stride</var>, size_t <var>n</var>, gsl_wavelet_workspace * <var>work</var>)</em></dt>
<dt><a name="index-gsl_005fwavelet_005ftransform_005finverse"></a>Function: <em>int</em> <strong>gsl_wavelet_transform_inverse</strong> <em>(const gsl_wavelet * <var>w</var>, double * <var>data</var>, size_t <var>stride</var>, size_t <var>n</var>, gsl_wavelet_workspace * <var>work</var>)</em></dt>
<dd>
<p>These functions compute in-place forward and inverse discrete wavelet
transforms of length <var>n</var> with stride <var>stride</var> on the array
<var>data</var>. The length of the transform <var>n</var> is restricted to powers
of two. For the <code>transform</code> version of the function the argument
<var>dir</var> can be either <code>forward</code> (<em>+1</em>) or <code>backward</code>
(<em>-1</em>). A workspace <var>work</var> of length <var>n</var> must be provided.
</p>
<p>For the forward transform, the elements of the original array are
replaced by the discrete wavelet
transform <em>f_i -> w_{j,k}</em>
in a packed triangular storage layout,
where <var>j</var> is the index of the level
<em>j = 0 ... J-1</em>
and
<var>k</var> is the index of the coefficient within each level,
<em>k = 0 ... (2^j)-1</em>.
The total number of levels is <em>J = \log_2(n)</em>. The output data
has the following form,
</p>
<div class="example">
<pre class="example">(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})
</pre></div>
<p>where the first element is the smoothing coefficient <em>s_{-1,0}</em>, followed by the detail coefficients <em>d_{j,k}</em> for each level
<em>j</em>. The backward transform inverts these coefficients to obtain
the original data.
</p>
<p>These functions return a status of <code>GSL_SUCCESS</code> upon successful
completion. <code>GSL_EINVAL</code> is returned if <var>n</var> is not an integer
power of 2 or if insufficient workspace is provided.
</p></dd></dl>
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