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<div class="section" id="torch-fft-fftn">
<h1>torch.fft.fftn<a class="headerlink" href="#torch-fft-fftn" title="Permalink to this headline">¶</a></h1>
<dl class="py function">
<dt id="torch.fft.fftn">
<code class="sig-prename descclassname"><span class="pre">torch.fft.</span></code><code class="sig-name descname"><span class="pre">fftn</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">s</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">None</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.fftn" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the N 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: <code class="docutils literal notranslate"><span class="pre">X[i_1,</span> <span class="pre">...,</span> <span class="pre">i_n]</span> <span class="pre">=</span> <span class="pre">conj(X[-i_1,</span> <span class="pre">...,</span> <span class="pre">-i_n])</span></code>. This
function always returns all positive and negative frequency terms even
though, for real inputs, half of these values are redundant.
<a class="reference internal" href="torch.fft.rfftn.html#torch.fft.rfftn" title="torch.fft.rfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfftn()</span></code></a> returns the more compact one-sided representation
where only the positive frequencies of the last dimension 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>s</strong> (<em>Tuple</em><em>[</em><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>, </em><em>optional</em>) – Signal size in the transformed dimensions.
If given, each dimension <code class="docutils literal notranslate"><span class="pre">dim[i]</span></code> will either be zero-padded or
trimmed to the length <code class="docutils literal notranslate"><span class="pre">s[i]</span></code> before computing the FFT.
If a length <code class="docutils literal notranslate"><span class="pre">-1</span></code> is specified, no padding is done in that dimension.
Default: <code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">=</span> <span class="pre">[input.size(d)</span> <span class="pre">for</span> <span class="pre">d</span> <span class="pre">in</span> <span class="pre">dim]</span></code></p></li>
<li><p><strong>dim</strong> (<em>Tuple</em><em>[</em><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>, </em><em>optional</em>) – Dimensions to be transformed.
Default: all dimensions, or the last <code class="docutils literal notranslate"><span class="pre">len(s)</span></code> dimensions if <code class="xref py py-attr docutils literal notranslate"><span class="pre">s</span></code> is given.</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.fftn" title="torch.fft.fftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">fftn()</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>Where <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">=</span> <span class="pre">prod(s)</span></code> is the logical FFT size.
Calling the backward transform (<a class="reference internal" href="torch.fft.ifftn.html#torch.fft.ifftn" title="torch.fft.ifftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifftn()</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.ifftn.html#torch.fft.ifftn" title="torch.fft.ifftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifftn()</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">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">complex64</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">fftn</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftn</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
<p>The discrete Fourier transform is separable, so <a class="reference internal" href="#torch.fft.fftn" title="torch.fft.fftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">fftn()</span></code></a>
here is equivalent to two one-dimensional <a class="reference internal" href="torch.fft.fft.html#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a> calls:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">two_ffts</span> <span class="o">=</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">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">x</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">assert_close</span><span class="p">(</span><span class="n">fftn</span><span class="p">,</span> <span class="n">two_ffts</span><span class="p">,</span> <span class="n">check_stride</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
</pre></div>
</div>
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