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<div class="section" id="the-wavelet-object">
<span id="reg-wavelet"></span><h1>The Wavelet object<a class="headerlink" href="#the-wavelet-object" title="Permalink to this headline">¶</a></h1>
<div class="section" id="wavelet-families-and-builtin-wavelets-names">
<h2>Wavelet families and builtin Wavelets names<a class="headerlink" href="#wavelet-families-and-builtin-wavelets-names" title="Permalink to this headline">¶</a></h2>
<p><a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet" title="pywt.Wavelet"><code class="xref py py-class docutils literal notranslate"><span class="pre">Wavelet</span></code></a> objects are really a handy carriers of a bunch of DWT-specific
data like <em>quadrature mirror filters</em> and some general properties associated
with them.</p>
<p>At first let’s go through the methods of creating a <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet" title="pywt.Wavelet"><code class="xref py py-class docutils literal notranslate"><span class="pre">Wavelet</span></code></a> object.
The easiest and the most convenient way is to use builtin named Wavelets.</p>
<p>These wavelets are organized into groups called wavelet families. The most
commonly used families are:</p>
<div class="highlight-default 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">pywt</span><span class="o">.</span><span class="n">families</span><span class="p">()</span>
<span class="go">['haar', 'db', 'sym', 'coif', 'bior', 'rbio', 'dmey', 'gaus', 'mexh', 'morl', 'cgau', 'shan', 'fbsp', 'cmor']</span>
</pre></div>
</div>
<p>The <a class="reference internal" href="../ref/wavelets.html#pywt.wavelist" title="pywt.wavelist"><code class="xref py py-func docutils literal notranslate"><span class="pre">wavelist()</span></code></a> function with family name passed as an argument is used to
obtain the list of wavelet names in each family.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">for</span> <span class="n">family</span> <span class="ow">in</span> <span class="n">pywt</span><span class="o">.</span><span class="n">families</span><span class="p">():</span>
<span class="gp">... </span> <span class="nb">print</span><span class="p">(</span><span class="s2">"</span><span class="si">%s</span><span class="s2"> family: "</span> <span class="o">%</span> <span class="n">family</span> <span class="o">+</span> <span class="s1">', '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">pywt</span><span class="o">.</span><span class="n">wavelist</span><span class="p">(</span><span class="n">family</span><span class="p">)))</span>
<span class="go">haar family: haar</span>
<span class="go">db family: db1, db2, db3, db4, db5, db6, db7, db8, db9, db10, db11, db12, db13, db14, db15, db16, db17, db18, db19, db20, db21, db22, db23, db24, db25, db26, db27, db28, db29, db30, db31, db32, db33, db34, db35, db36, db37, db38</span>
<span class="go">sym family: sym2, sym3, sym4, sym5, sym6, sym7, sym8, sym9, sym10, sym11, sym12, sym13, sym14, sym15, sym16, sym17, sym18, sym19, sym20</span>
<span class="go">coif family: coif1, coif2, coif3, coif4, coif5, coif6, coif7, coif8, coif9, coif10, coif11, coif12, coif13, coif14, coif15, coif16, coif17</span>
<span class="go">bior family: bior1.1, bior1.3, bior1.5, bior2.2, bior2.4, bior2.6, bior2.8, bior3.1, bior3.3, bior3.5, bior3.7, bior3.9, bior4.4, bior5.5, bior6.8</span>
<span class="go">rbio family: rbio1.1, rbio1.3, rbio1.5, rbio2.2, rbio2.4, rbio2.6, rbio2.8, rbio3.1, rbio3.3, rbio3.5, rbio3.7, rbio3.9, rbio4.4, rbio5.5, rbio6.8</span>
<span class="go">dmey family: dmey</span>
<span class="go">gaus family: gaus1, gaus2, gaus3, gaus4, gaus5, gaus6, gaus7, gaus8</span>
<span class="go">mexh family: mexh</span>
<span class="go">morl family: morl</span>
<span class="go">cgau family: cgau1, cgau2, cgau3, cgau4, cgau5, cgau6, cgau7, cgau8</span>
<span class="go">shan family: shan</span>
<span class="go">fbsp family: fbsp</span>
<span class="go">cmor family: cmor</span>
</pre></div>
</div>
<p>To get the full list of builtin wavelets’ names just use the <a class="reference internal" href="../ref/wavelets.html#pywt.wavelist" title="pywt.wavelist"><code class="xref py py-func docutils literal notranslate"><span class="pre">wavelist()</span></code></a>
with no argument.</p>
</div>
<div class="section" id="creating-wavelet-objects">
<h2>Creating Wavelet objects<a class="headerlink" href="#creating-wavelet-objects" title="Permalink to this headline">¶</a></h2>
<p>Now when we know all the names let’s finally create a <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet" title="pywt.Wavelet"><code class="xref py py-class docutils literal notranslate"><span class="pre">Wavelet</span></code></a> object:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">w</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">Wavelet</span><span class="p">(</span><span class="s1">'db3'</span><span class="p">)</span>
</pre></div>
</div>
<p>So.. that’s it.</p>
</div>
<div class="section" id="wavelet-properties">
<h2>Wavelet properties<a class="headerlink" href="#wavelet-properties" title="Permalink to this headline">¶</a></h2>
<p>But what can we do with <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet" title="pywt.Wavelet"><code class="xref py py-class docutils literal notranslate"><span class="pre">Wavelet</span></code></a> objects? Well, they carry some
interesting information.</p>
<p>First, let’s try printing a <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet" title="pywt.Wavelet"><code class="xref py py-class docutils literal notranslate"><span class="pre">Wavelet</span></code></a> object. This shows a brief
information about its name, its family name and some properties like
orthogonality and symmetry.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="go">Wavelet db3</span>
<span class="go"> Family name: Daubechies</span>
<span class="go"> Short name: db</span>
<span class="go"> Filters length: 6</span>
<span class="go"> Orthogonal: True</span>
<span class="go"> Biorthogonal: True</span>
<span class="go"> Symmetry: asymmetric</span>
<span class="go"> DWT: True</span>
<span class="go"> CWT: False</span>
</pre></div>
</div>
<p>But the most important information are the wavelet filters coefficients, which
are used in <a class="reference internal" href="../ref/dwt-discrete-wavelet-transform.html#ref-dwt"><span class="std std-ref">Discrete Wavelet Transform</span></a>. These coefficients can
be obtained via the <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.dec_lo" title="pywt.Wavelet.dec_lo"><code class="xref py py-attr docutils literal notranslate"><span class="pre">dec_lo</span></code></a>, <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.dec_hi" title="pywt.Wavelet.dec_hi"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Wavelet.dec_hi</span></code></a>,
<a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.rec_lo" title="pywt.Wavelet.rec_lo"><code class="xref py py-attr docutils literal notranslate"><span class="pre">rec_lo</span></code></a> and <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.rec_hi" title="pywt.Wavelet.rec_hi"><code class="xref py py-attr docutils literal notranslate"><span class="pre">rec_hi</span></code></a> attributes, which
corresponds to lowpass and highpass decomposition filters and lowpass and
highpass reconstruction filters respectively:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">def</span> <span class="nf">print_array</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="gp">... </span> <span class="nb">print</span><span class="p">(</span><span class="s2">"[</span><span class="si">%s</span><span class="s2">]"</span> <span class="o">%</span> <span class="s2">", "</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="s2">"</span><span class="si">%.14f</span><span class="s2">"</span> <span class="o">%</span> <span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">arr</span><span class="p">]))</span>
</pre></div>
</div>
<p>Another way to get the filters data is to use the <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.filter_bank" title="pywt.Wavelet.filter_bank"><code class="xref py py-attr docutils literal notranslate"><span class="pre">filter_bank</span></code></a>
attribute, which returns all four filters in a tuple:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">filter_bank</span> <span class="o">==</span> <span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">dec_lo</span><span class="p">,</span> <span class="n">w</span><span class="o">.</span><span class="n">dec_hi</span><span class="p">,</span> <span class="n">w</span><span class="o">.</span><span class="n">rec_lo</span><span class="p">,</span> <span class="n">w</span><span class="o">.</span><span class="n">rec_hi</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
<p>Other Wavelet’s properties are:</p>
<blockquote>
<div><p>Wavelet <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.name" title="pywt.Wavelet.name"><code class="xref py py-attr docutils literal notranslate"><span class="pre">name</span></code></a>, <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.short_family_name" title="pywt.Wavelet.short_family_name"><code class="xref py py-attr docutils literal notranslate"><span class="pre">short_family_name</span></code></a> and <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.family_name" title="pywt.Wavelet.family_name"><code class="xref py py-attr docutils literal notranslate"><span class="pre">family_name</span></code></a>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
<span class="go">db3</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">short_family_name</span><span class="p">)</span>
<span class="go">db</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">family_name</span><span class="p">)</span>
<span class="go">Daubechies</span>
</pre></div>
</div>
<ul>
<li><p class="first">Decomposition (<a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.dec_len" title="pywt.Wavelet.dec_len"><code class="xref py py-attr docutils literal notranslate"><span class="pre">dec_len</span></code></a>) and reconstruction
(<a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.rec_len" title="pywt.Wavelet.rec_len"><code class="xref py py-attr docutils literal notranslate"><span class="pre">rec_len</span></code></a>) filter lengths:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">int</span><span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">dec_len</span><span class="p">)</span> <span class="c1"># int() is for normalizing longs and ints for doctest</span>
<span class="go">6</span>
<span class="gp">>>> </span><span class="nb">int</span><span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">rec_len</span><span class="p">)</span>
<span class="go">6</span>
</pre></div>
</div>
</li>
<li><p class="first">Orthogonality (<a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.orthogonal" title="pywt.Wavelet.orthogonal"><code class="xref py py-attr docutils literal notranslate"><span class="pre">orthogonal</span></code></a>) and biorthogonality (<a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.biorthogonal" title="pywt.Wavelet.biorthogonal"><code class="xref py py-attr docutils literal notranslate"><span class="pre">biorthogonal</span></code></a>):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">orthogonal</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">biorthogonal</span>
<span class="go">True</span>
</pre></div>
</div>
</li>
<li><p class="first">Symmetry (<a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.symmetry" title="pywt.Wavelet.symmetry"><code class="xref py py-attr docutils literal notranslate"><span class="pre">symmetry</span></code></a>):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">symmetry</span><span class="p">)</span>
<span class="go">asymmetric</span>
</pre></div>
</div>
</li>
<li><p class="first">Number of vanishing moments for the scaling function <code class="docutils literal notranslate"><span class="pre">phi</span></code>
(<a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.vanishing_moments_phi" title="pywt.Wavelet.vanishing_moments_phi"><code class="xref py py-attr docutils literal notranslate"><span class="pre">vanishing_moments_phi</span></code></a>) and the wavelet function <code class="docutils literal notranslate"><span class="pre">psi</span></code>
(<a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.vanishing_moments_psi" title="pywt.Wavelet.vanishing_moments_psi"><code class="xref py py-attr docutils literal notranslate"><span class="pre">vanishing_moments_psi</span></code></a>) associated with the filters:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">vanishing_moments_phi</span>
<span class="go">0</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">vanishing_moments_psi</span>
<span class="go">3</span>
</pre></div>
</div>
</li>
</ul>
</div></blockquote>
<p>Now when we know a bit about the builtin Wavelets, let’s see how to create
<a class="reference internal" href="../ref/wavelets.html#custom-wavelets"><span class="std std-ref">custom Wavelets</span></a> objects. These can be done in two ways:</p>
<blockquote>
<div><ol class="arabic">
<li><p class="first">Passing the filter bank object that implements the <code class="docutils literal notranslate"><span class="pre">filter_bank</span></code>
attribute. The attribute must return four filters coefficients.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">class</span> <span class="nc">MyHaarFilterBank</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="gp">... </span> <span class="nd">@property</span>
<span class="gp">... </span> <span class="k">def</span> <span class="nf">filter_bank</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="gp">... </span> <span class="kn">from</span> <span class="nn">math</span> <span class="k">import</span> <span class="n">sqrt</span>
<span class="gp">... </span> <span class="k">return</span> <span class="p">([</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">])</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">my_wavelet</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">Wavelet</span><span class="p">(</span><span class="s1">'My Haar Wavelet'</span><span class="p">,</span> <span class="n">filter_bank</span><span class="o">=</span><span class="n">MyHaarFilterBank</span><span class="p">())</span>
</pre></div>
</div>
</li>
<li><p class="first">Passing the filters coefficients directly as the <code class="docutils literal notranslate"><span class="pre">filter_bank</span></code>
parameter.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">math</span> <span class="k">import</span> <span class="n">sqrt</span>
<span class="gp">>>> </span><span class="n">my_filter_bank</span> <span class="o">=</span> <span class="p">([</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">my_wavelet</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">Wavelet</span><span class="p">(</span><span class="s1">'My Haar Wavelet'</span><span class="p">,</span> <span class="n">filter_bank</span><span class="o">=</span><span class="n">my_filter_bank</span><span class="p">)</span>
</pre></div>
</div>
</li>
</ol>
</div></blockquote>
<p>Note that such custom wavelets <strong>will not</strong> have all the properties set
to correct values:</p>
<blockquote>
<div><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">my_wavelet</span><span class="p">)</span>
<span class="go">Wavelet My Haar Wavelet</span>
<span class="go"> Family name:</span>
<span class="go"> Short name:</span>
<span class="go"> Filters length: 2</span>
<span class="go"> Orthogonal: False</span>
<span class="go"> Biorthogonal: False</span>
<span class="go"> Symmetry: unknown</span>
<span class="go"> DWT: True</span>
<span class="go"> CWT: False</span>
</pre></div>
</div>
<p>You can however set a couple of them on your own:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">my_wavelet</span><span class="o">.</span><span class="n">orthogonal</span> <span class="o">=</span> <span class="kc">True</span>
<span class="gp">>>> </span><span class="n">my_wavelet</span><span class="o">.</span><span class="n">biorthogonal</span> <span class="o">=</span> <span class="kc">True</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">my_wavelet</span><span class="p">)</span>
<span class="go">Wavelet My Haar Wavelet</span>
<span class="go"> Family name:</span>
<span class="go"> Short name:</span>
<span class="go"> Filters length: 2</span>
<span class="go"> Orthogonal: True</span>
<span class="go"> Biorthogonal: True</span>
<span class="go"> Symmetry: unknown</span>
<span class="go"> DWT: True</span>
<span class="go"> CWT: False</span>
</pre></div>
</div>
</div></blockquote>
</div>
<div class="section" id="and-now-the-wavefun">
<h2>And now… the <code class="docutils literal notranslate"><span class="pre">wavefun</span></code>!<a class="headerlink" href="#and-now-the-wavefun" title="Permalink to this headline">¶</a></h2>
<p>We all know that the fun with wavelets is in wavelet functions.
Now what would be this package without a tool to compute wavelet
and scaling functions approximations?</p>
<p>This is the purpose of the <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.wavefun" title="pywt.Wavelet.wavefun"><code class="xref py py-meth docutils literal notranslate"><span class="pre">wavefun()</span></code></a> method, which is used to
approximate scaling function (<code class="docutils literal notranslate"><span class="pre">phi</span></code>) and wavelet function (<code class="docutils literal notranslate"><span class="pre">psi</span></code>) at the
given level of refinement, based on the filters coefficients.</p>
<p>The number of returned values varies depending on the wavelet’s
orthogonality property. For orthogonal wavelets the result is tuple
with scaling function, wavelet function and xgrid coordinates.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">w</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">Wavelet</span><span class="p">(</span><span class="s1">'sym3'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">orthogonal</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="p">(</span><span class="n">phi</span><span class="p">,</span> <span class="n">psi</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="n">w</span><span class="o">.</span><span class="n">wavefun</span><span class="p">(</span><span class="n">level</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
</div>
<p>For biorthogonal (non-orthogonal) wavelets different scaling and wavelet
functions are used for decomposition and reconstruction, and thus five
elements are returned: decomposition scaling and wavelet functions
approximations, reconstruction scaling and wavelet functions approximations,
and the xgrid.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">w</span> <span class="o">=</span> <span class="n">pywt</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="n">w</span><span class="o">.</span><span class="n">orthogonal</span>
<span class="go">False</span>
<span class="gp">>>> </span><span class="p">(</span><span class="n">phi_d</span><span class="p">,</span> <span class="n">psi_d</span><span class="p">,</span> <span class="n">phi_r</span><span class="p">,</span> <span class="n">psi_r</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="n">w</span><span class="o">.</span><span class="n">wavefun</span><span class="p">(</span><span class="n">level</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last">You can find live examples of <a class="reference internal" href="../ref/wavelets.html#pywt.Wavelet.wavefun" title="pywt.Wavelet.wavefun"><code class="xref py py-meth docutils literal notranslate"><span class="pre">wavefun()</span></code></a> usage and
images of all the built-in wavelets on the
<a class="reference external" href="http://wavelets.pybytes.com">Wavelet Properties Browser</a> page.
However, <strong>this website is no longer actively maintained</strong> and does not
include every wavelet present in PyWavelets. The precision of the wavelet
coefficients at that site is also lower than those included in
PyWavelets.</p>
</div>
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<li><a class="reference internal" href="#creating-wavelet-objects">Creating Wavelet objects</a></li>
<li><a class="reference internal" href="#wavelet-properties">Wavelet properties</a></li>
<li><a class="reference internal" href="#and-now-the-wavefun">And now… the <code class="docutils literal notranslate"><span class="pre">wavefun</span></code>!</a></li>
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