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<div class="section" id="other-functions">
<span id="ref-other"></span><h1>Other functions<a class="headerlink" href="#other-functions" title="Permalink to this headline">¶</a></h1>
<div class="section" id="integrating-wavelet-functions">
<h2>Integrating wavelet functions<a class="headerlink" href="#integrating-wavelet-functions" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="pywt.integrate_wavelet">
<code class="descclassname">pywt.</code><code class="descname">integrate_wavelet</code><span class="sig-paren">(</span><em>wavelet</em>, <em>precision=8</em><span class="sig-paren">)</span><a class="headerlink" href="#pywt.integrate_wavelet" title="Permalink to this definition">¶</a></dt>
<dd><p>Integrate <cite>psi</cite> wavelet function from -Inf to x using the rectangle
integration method.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>wavelet</strong> <span class="classifier-delimiter">:</span> <span class="classifier">Wavelet instance or str</span></dt>
<dd><p class="first last">Wavelet to integrate. If a string, should be the name of a wavelet.</p>
</dd>
<dt><strong>precision</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int, optional</span></dt>
<dd><p class="first last">Precision that will be used for wavelet function
approximation computed with the wavefun(level=precision)
Wavelet’s method (default: 8).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>[int_psi, x] :</strong></dt>
<dd><p class="first last">for orthogonal wavelets</p>
</dd>
<dt><strong>[int_psi_d, int_psi_r, x] :</strong></dt>
<dd><p class="first last">for other wavelets</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pywt</span> <span class="k">import</span> <span class="n">Wavelet</span><span class="p">,</span> <span class="n">integrate_wavelet</span>
<span class="gp">>>> </span><span class="n">wavelet1</span> <span class="o">=</span> <span class="n">Wavelet</span><span class="p">(</span><span class="s1">'db2'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="p">[</span><span class="n">int_psi</span><span class="p">,</span> <span class="n">x</span><span class="p">]</span> <span class="o">=</span> <span class="n">integrate_wavelet</span><span class="p">(</span><span class="n">wavelet1</span><span class="p">,</span> <span class="n">precision</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">wavelet2</span> <span class="o">=</span> <span class="n">Wavelet</span><span class="p">(</span><span class="s1">'bior1.3'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="p">[</span><span class="n">int_psi_d</span><span class="p">,</span> <span class="n">int_psi_r</span><span class="p">,</span> <span class="n">x</span><span class="p">]</span> <span class="o">=</span> <span class="n">integrate_wavelet</span><span class="p">(</span><span class="n">wavelet2</span><span class="p">,</span> <span class="n">precision</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<p>The result of the call depends on the <code class="docutils literal notranslate"><span class="pre">wavelet</span></code> argument:</p>
<ul>
<li><p class="first">for orthogonal and continuous wavelets - an integral of the
wavelet function specified on an x-grid:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">int_psi</span><span class="p">,</span> <span class="n">x_grid</span><span class="p">]</span> <span class="o">=</span> <span class="n">integrate_wavelet</span><span class="p">(</span><span class="n">wavelet</span><span class="p">,</span> <span class="n">precision</span><span class="p">)</span>
</pre></div>
</div>
</li>
<li><p class="first">for other wavelets - integrals of decomposition and
reconstruction wavelet functions and a corresponding x-grid:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">int_psi_d</span><span class="p">,</span> <span class="n">int_psi_r</span><span class="p">,</span> <span class="n">x_grid</span><span class="p">]</span> <span class="o">=</span> <span class="n">integrate_wavelet</span><span class="p">(</span><span class="n">wavelet</span><span class="p">,</span> <span class="n">precision</span><span class="p">)</span>
</pre></div>
</div>
</li>
</ul>
</div>
<div class="section" id="central-frequency-of-psi-wavelet-function">
<h2>Central frequency of <code class="docutils literal notranslate"><span class="pre">psi</span></code> wavelet function<a class="headerlink" href="#central-frequency-of-psi-wavelet-function" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="pywt.central_frequency">
<code class="descclassname">pywt.</code><code class="descname">central_frequency</code><span class="sig-paren">(</span><em>wavelet</em>, <em>precision=8</em><span class="sig-paren">)</span><a class="headerlink" href="#pywt.central_frequency" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the central frequency of the <cite>psi</cite> wavelet function.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>wavelet</strong> <span class="classifier-delimiter">:</span> <span class="classifier">Wavelet instance, str or tuple</span></dt>
<dd><p class="first last">Wavelet to integrate. If a string, should be the name of a wavelet.</p>
</dd>
<dt><strong>precision</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int, optional</span></dt>
<dd><p class="first last">Precision that will be used for wavelet function
approximation computed with the wavefun(level=precision)
Wavelet’s method (default: 8).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>scalar</strong></dt>
<dd></dd>
</dl>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="pywt.scale2frequency">
<code class="descclassname">pywt.</code><code class="descname">scale2frequency</code><span class="sig-paren">(</span><em>wavelet</em>, <em>scale</em>, <em>precision=8</em><span class="sig-paren">)</span><a class="headerlink" href="#pywt.scale2frequency" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>wavelet</strong> <span class="classifier-delimiter">:</span> <span class="classifier">Wavelet instance or str</span></dt>
<dd><p class="first last">Wavelet to integrate. If a string, should be the name of a wavelet.</p>
</dd>
<dt><strong>scale</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd></dd>
<dt><strong>precision</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int, optional</span></dt>
<dd><p class="first last">Precision that will be used for wavelet function approximation computed
with <code class="docutils literal notranslate"><span class="pre">wavelet.wavefun(level=precision)</span></code>. Default is 8.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>freq</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd></dd>
</dl>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
<div class="section" id="quadrature-mirror-filter">
<h2>Quadrature Mirror Filter<a class="headerlink" href="#quadrature-mirror-filter" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="pywt.qmf">
<code class="descclassname">pywt.</code><code class="descname">qmf</code><span class="sig-paren">(</span><em>filt</em><span class="sig-paren">)</span><a class="headerlink" href="#pywt.qmf" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the Quadrature Mirror Filter(QMF).</p>
<p>The magnitude response of QMF is mirror image about <cite>pi/2</cite> of that of the
input filter.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>filt</strong> <span class="classifier-delimiter">:</span> <span class="classifier">array_like</span></dt>
<dd><p class="first last">Input filter for which QMF needs to be computed.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>qm_filter</strong> <span class="classifier-delimiter">:</span> <span class="classifier">ndarray</span></dt>
<dd><p class="first last">Quadrature mirror of the input filter.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
<div class="section" id="orthogonal-filter-banks">
<h2>Orthogonal Filter Banks<a class="headerlink" href="#orthogonal-filter-banks" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="pywt.orthogonal_filter_bank">
<code class="descclassname">pywt.</code><code class="descname">orthogonal_filter_bank</code><span class="sig-paren">(</span><em>scaling_filter</em><span class="sig-paren">)</span><a class="headerlink" href="#pywt.orthogonal_filter_bank" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the orthogonal filter bank.</p>
<p>The orthogonal filter bank consists of the HPFs and LPFs at
decomposition and reconstruction stage for the input scaling filter.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>scaling_filter</strong> <span class="classifier-delimiter">:</span> <span class="classifier">array_like</span></dt>
<dd><p class="first last">Input scaling filter (father wavelet).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>orth_filt_bank</strong> <span class="classifier-delimiter">:</span> <span class="classifier">tuple of 4 ndarrays</span></dt>
<dd><p class="first last">The orthogonal filter bank of the input scaling filter in the order :
1] Decomposition LPF
2] Decomposition HPF
3] Reconstruction LPF
4] Reconstruction HPF</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
<div class="section" id="example-datasets">
<h2>Example Datasets<a class="headerlink" href="#example-datasets" title="Permalink to this headline">¶</a></h2>
<p>The following example datasets are available in the module <code class="docutils literal notranslate"><span class="pre">pywt.data</span></code>:</p>
<blockquote>
<div><table border="1" class="docutils">
<colgroup>
<col width="24%" />
<col width="76%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head"><strong>name</strong></th>
<th class="head"><strong>description</strong></th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>ecg</td>
<td>ECG waveform (1024 samples)</td>
</tr>
<tr class="row-odd"><td>aero</td>
<td>grayscale image (512x512)</td>
</tr>
<tr class="row-even"><td>ascent</td>
<td>grayscale image (512x512)</td>
</tr>
<tr class="row-odd"><td>camera</td>
<td>grayscale image (512x512)</td>
</tr>
<tr class="row-even"><td>nino</td>
<td>sea surface temperature (264 samples)</td>
</tr>
<tr class="row-odd"><td>demo_signal</td>
<td>various synthetic 1d test signals</td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>Each can be loaded via a function of the same name.</p>
<dl class="function">
<dt id="pywt.data.demo_signal">
<code class="descclassname">pywt.data.</code><code class="descname">demo_signal</code><span class="sig-paren">(</span><em>name='Bumps'</em>, <em>n=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pywt.data.demo_signal" title="Permalink to this definition">¶</a></dt>
<dd><p>Simple 1D wavelet test functions.</p>
<p>This function can generate a number of common 1D test signals used in
papers by David Donoho and colleagues (e.g. <a class="reference internal" href="#re2ac4194fcbd-1" id="id1">[1]</a>) as well as the wavelet
book by Stéphane Mallat <a class="reference internal" href="#re2ac4194fcbd-2" id="id2">[2]</a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>name</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{‘Blocks’, ‘Bumps’, ‘HeaviSine’, ‘Doppler’, …}</span></dt>
<dd><p class="first last">The type of test signal to generate (<cite>name</cite> is case-insensitive). If
<cite>name</cite> is set to <cite>‘list’</cite>, a list of the avialable test functions is
returned.</p>
</dd>
<dt><strong>n</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int or None</span></dt>
<dd><p class="first last">The length of the test signal. This should be provided for all test
signals except <cite>‘Gabor’</cite> and <cite>‘sineoneoverx’</cite> which have a fixed
length.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>f</strong> <span class="classifier-delimiter">:</span> <span class="classifier">np.ndarray</span></dt>
<dd><p class="first last">Array of length <code class="docutils literal notranslate"><span class="pre">n</span></code> corresponding to the specified test signal type.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>This function is a partial reimplementation of the <cite>MakeSignal</cite> function
from the [Wavelab](<a class="reference external" href="https://statweb.stanford.edu/~wavelab/">https://statweb.stanford.edu/~wavelab/</a>) toolbox. These
test signals are provided with permission of Dr. Donoho to encourage
reproducible research.</p>
<p class="rubric">References</p>
<table class="docutils citation" frame="void" id="re2ac4194fcbd-1" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[1]</td><td><em>(<a class="fn-backref" href="#id1">1</a>, <a class="fn-backref" href="#id3">2</a>)</em> D.L. Donoho and I.M. Johnstone. Ideal spatial adaptation by
wavelet shrinkage. Biometrika, vol. 81, pp. 425–455, 1994.</td></tr>
</tbody>
</table>
<table class="docutils citation" frame="void" id="re2ac4194fcbd-2" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[2]</td><td><em>(<a class="fn-backref" href="#id2">1</a>, <a class="fn-backref" href="#id4">2</a>)</em> S. Mallat. A Wavelet Tour of Signal Processing: The Sparse Way.
Academic Press. 2009.</td></tr>
</tbody>
</table>
</dd></dl>
<p><strong>Example:</strong></p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pywt</span>
<span class="gp">>>> </span><span class="n">camera</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">camera</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">doppler</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">demo_signal</span><span class="p">(</span><span class="s1">'doppler'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">available_signals</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">demo_signal</span><span class="p">(</span><span class="s1">'list'</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
</div>
</div>
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<h3><a href="../index.html">Table of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Other functions</a><ul>
<li><a class="reference internal" href="#integrating-wavelet-functions">Integrating wavelet functions</a></li>
<li><a class="reference internal" href="#central-frequency-of-psi-wavelet-function">Central frequency of <code class="docutils literal notranslate"><span class="pre">psi</span></code> wavelet function</a></li>
<li><a class="reference internal" href="#quadrature-mirror-filter">Quadrature Mirror Filter</a></li>
<li><a class="reference internal" href="#orthogonal-filter-banks">Orthogonal Filter Banks</a></li>
<li><a class="reference internal" href="#example-datasets">Example Datasets</a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
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title="previous chapter">Thresholding functions</a></p>
<h4>Next topic</h4>
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title="next chapter">Usage examples</a></p><div>
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<i><a href="https://github.com/PyWavelets/pywt/blob/master/doc/source/ref/other-functions.rst" target="_blank">
Other functions
</a></i> on GitHub.
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<li>
Press <b>Edit this file</b> button.
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<li>
Edit file contents using GitHub's text editor in your web browser
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Fill in the <b>Commit message</b> text box at the end of the page
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Press <b>Propose file change</b> button next to it when done.
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On <i>Send a pull request</i> page you don't need to fill in text
anymore. Just press <b>Send pull request</b> button.
</li>
<li>
Your changes are now queued for review under project's
<a href="https://github.com/PyWavelets/pywt/pulls" target="_blank">Pull requests</a> tab
on Github.
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