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<div class="section" id="torch-fft-fft">
<h1>torch.fft.fft<a class="headerlink" href="#torch-fft-fft" title="Permalink to this headline">¶</a></h1>
<dl class="py function">
<dt id="torch.fft.fft">
<code class="sig-prename descclassname"><span class="pre">torch.fft.</span></code><code class="sig-name descname"><span class="pre">fft</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">input</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">-</span> <span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> → <span class="pre">Tensor</span><a class="headerlink" href="#torch.fft.fft" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the one dimensional discrete Fourier transform of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The Fourier domain representation of any real signal satisfies the
Hermitian property: <cite>X[i] = conj(X[-i])</cite>. This function always returns both
the positive and negative frequency terms even though, for real inputs, the
negative frequencies are redundant. <a class="reference internal" href="torch.fft.rfft.html#torch.fft.rfft" title="torch.fft.rfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft()</span></code></a> returns the
more compact one-sided representation where only the positive frequencies
are returned.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>n</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.10)"><em>int</em></a><em>, </em><em>optional</em>) – Signal length. If given, the input will either be zero-padded
or trimmed to this length before computing the FFT.</p></li>
<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.10)"><em>int</em></a><em>, </em><em>optional</em>) – The dimension along which to take the one dimensional FFT.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.10)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the forward transform
(<a class="reference internal" href="#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the FFT orthonormal)</p></li>
</ul>
<p>Calling the backward transform (<a class="reference internal" href="torch.fft.ifft.html#torch.fft.ifft" title="torch.fft.ifft"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="torch.fft.ifft.html#torch.fft.ifft" title="torch.fft.ifft"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (no normalization).</p>
</p></li>
</ul>
</dd>
<dt class="field-even">Keyword Arguments</dt>
<dd class="field-even"><p><strong>out</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a><em>, </em><em>optional</em>) – the output tensor.</p>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">t</span>
<span class="go">tensor([0, 1, 2, 3])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="go">tensor([ 6.+0.j, -2.+2.j, -2.+0.j, -2.-2.j])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">0.</span><span class="o">+</span><span class="mf">1.</span><span class="n">j</span><span class="p">,</span> <span class="mf">2.</span><span class="o">+</span><span class="mf">3.</span><span class="n">j</span><span class="p">,</span> <span class="mf">4.</span><span class="o">+</span><span class="mf">5.</span><span class="n">j</span><span class="p">,</span> <span class="mf">6.</span><span class="o">+</span><span class="mf">7.</span><span class="n">j</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="go">tensor([12.+16.j, -8.+0.j, -4.-4.j, 0.-8.j])</span>
</pre></div>
</div>
</dd></dl>
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