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<div class="section" id="torch-blackman-window">
<h1>torch.blackman_window<a class="headerlink" href="#torch-blackman-window" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.blackman_window">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">blackman_window</code><span class="sig-paren">(</span><em class="sig-param">window_length</em>, <em class="sig-param">periodic=True</em>, <em class="sig-param">dtype=None</em>, <em class="sig-param">layout=torch.strided</em>, <em class="sig-param">device=None</em>, <em class="sig-param">requires_grad=False</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.blackman_window" title="Permalink to this definition">¶</a></dt>
<dd><p>Blackman window function.</p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>w</mi><mo stretchy="false">[</mo><mi>n</mi><mo stretchy="false">]</mo><mo>=</mo><mn>0.42</mn><mo>−</mo><mn>0.5</mn><mi>cos</mi><mo></mo><mrow><mo fence="true">(</mo><mfrac><mrow><mn>2</mn><mi>π</mi><mi>n</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>+</mo><mn>0.08</mn><mi>cos</mi><mo></mo><mrow><mo fence="true">(</mo><mfrac><mrow><mn>4</mn><mi>π</mi><mi>n</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">w[n] = 0.42 - 0.5 \cos \left( \frac{2 \pi n}{N - 1} \right) + 0.08 \cos \left( \frac{4 \pi n}{N - 1} \right)
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mopen">[</span><span class="mord mathnormal">n</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">4</span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">5</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">0</span><span class="mord">8</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span></span></span></span></span>
</div><p>where <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span>
</span> is the full window size.</p>
<p>The input <code class="xref py py-attr docutils literal notranslate"><span class="pre">window_length</span></code> is a positive integer controlling the
returned window size. <code class="xref py py-attr docutils literal notranslate"><span class="pre">periodic</span></code> flag determines whether the returned
window trims off the last duplicate value from the symmetric window and is
ready to be used as a periodic window with functions like
<a class="reference internal" href="torch.stft.html#torch.stft" title="torch.stft"><code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.stft()</span></code></a>. Therefore, if <code class="xref py py-attr docutils literal notranslate"><span class="pre">periodic</span></code> is true, the <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span>
</span> in
above formula is in fact <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>window_length</mtext><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\text{window\_length} + 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.00444em;vertical-align:-0.31em;"></span><span class="mord text"><span class="mord">window_length</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>
</span>. Also, we always have
<code class="docutils literal notranslate"><span class="pre">torch.blackman_window(L,</span> <span class="pre">periodic=True)</span></code> equal to
<code class="docutils literal notranslate"><span class="pre">torch.blackman_window(L</span> <span class="pre">+</span> <span class="pre">1,</span> <span class="pre">periodic=False)[:-1])</span></code>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>If <code class="xref py py-attr docutils literal notranslate"><span class="pre">window_length</span></code> <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>
</span>, the returned window contains a single value 1.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>window_length</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.8)"><em>int</em></a>) – the size of returned window</p></li>
<li><p><strong>periodic</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.8)"><em>bool</em></a><em>, </em><em>optional</em>) – If True, returns a window to be used as periodic
function. If False, return a symmetric window.</p></li>
<li><p><strong>dtype</strong> (<a class="reference internal" href="../tensor_attributes.html#torch.torch.dtype" title="torch.torch.dtype"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.dtype</span></code></a>, optional) – the desired data type of returned tensor.
Default: if <code class="docutils literal notranslate"><span class="pre">None</span></code>, uses a global default (see <a class="reference internal" href="torch.set_default_tensor_type.html#torch.set_default_tensor_type" title="torch.set_default_tensor_type"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.set_default_tensor_type()</span></code></a>). Only floating point types are supported.</p></li>
<li><p><strong>layout</strong> (<a class="reference internal" href="../tensor_attributes.html#torch.torch.layout" title="torch.torch.layout"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.layout</span></code></a>, optional) – the desired layout of returned window tensor. Only
<code class="docutils literal notranslate"><span class="pre">torch.strided</span></code> (dense layout) is supported.</p></li>
<li><p><strong>device</strong> (<a class="reference internal" href="../tensor_attributes.html#torch.torch.device" title="torch.torch.device"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.device</span></code></a>, optional) – the desired device of returned tensor.
Default: if <code class="docutils literal notranslate"><span class="pre">None</span></code>, uses the current device for the default tensor type
(see <a class="reference internal" href="torch.set_default_tensor_type.html#torch.set_default_tensor_type" title="torch.set_default_tensor_type"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.set_default_tensor_type()</span></code></a>). <code class="xref py py-attr docutils literal notranslate"><span class="pre">device</span></code> will be the CPU
for CPU tensor types and the current CUDA device for CUDA tensor types.</p></li>
<li><p><strong>requires_grad</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.8)"><em>bool</em></a><em>, </em><em>optional</em>) – If autograd should record operations on the
returned tensor. Default: <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>A 1-D tensor of size <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mtext>window_length</mtext><mo separator="true">,</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\text{window\_length},)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord">window_length</span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mclose">)</span></span></span></span>
</span> containing the window</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p><a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor">Tensor</a></p>
</dd>
</dl>
</dd></dl>
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