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<div class="section" id="torch-fft">
<h1>torch.fft<a class="headerlink" href="#torch-fft" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.fft">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">fft</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">signal_ndim</em>, <em class="sig-param">normalized=False</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft" title="Permalink to this definition">¶</a></dt>
<dd><p>Complex-to-complex Discrete Fourier Transform.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>The function <a class="reference internal" href="#torch.fft" title="torch.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.fft()</span></code></a> is deprecated and will be removed in
PyTorch 1.8. Use the new <a class="reference internal" href="../fft.html#torch-fft-module"><span class="std std-ref">torch.fft</span></a> module
functions, instead, by importing <a class="reference internal" href="../fft.html#torch-fft-module"><span class="std std-ref">torch.fft</span></a> and
calling <a class="reference internal" href="../fft.html#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.fft.fft()</span></code></a> or <a class="reference internal" href="../fft.html#torch.fft.fftn" title="torch.fft.fftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.fft.fftn()</span></code></a>.</p>
</div>
<p>This method computes the complex-to-complex discrete Fourier transform.
Ignoring the batch dimensions, it computes the following expression:</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>X</mi><mo stretchy="false">[</mo><msub><mi>ω</mi><mn>1</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>ω</mi><mi>d</mi></msub><mo stretchy="false">]</mo><mo>=</mo><munderover><mo>∑</mo><mrow><msub><mi>n</mi><mn>1</mn></msub><mo>=</mo><mn>0</mn></mrow><mrow><msub><mi>N</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn></mrow></munderover><mo>⋯</mo><munderover><mo>∑</mo><mrow><msub><mi>n</mi><mi>d</mi></msub><mo>=</mo><mn>0</mn></mrow><mrow><msub><mi>N</mi><mi>d</mi></msub><mo>−</mo><mn>1</mn></mrow></munderover><mi>x</mi><mo stretchy="false">[</mo><msub><mi>n</mi><mn>1</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>n</mi><mi>d</mi></msub><mo stretchy="false">]</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>j</mi><mtext> </mtext><mn>2</mn><mi>π</mi><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>d</mi></munderover><mfrac><mrow><msub><mi>ω</mi><mi>i</mi></msub><msub><mi>n</mi><mi>i</mi></msub></mrow><msub><mi>N</mi><mi>i</mi></msub></mfrac></mrow></msup><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">X[\omega_1, \dots, \omega_d] =
\sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x[n_1, \dots, n_d]
e^{-j\ 2 \pi \sum_{i=0}^d \frac{\omega_i n_i}{N_i}},
</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:0.07847em;">X</span><span class="mopen">[</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></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:3.2181690000000005em;vertical-align:-1.3729729999999998em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8394360000000005em;"><span style="top:-1.8828870000000002em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mrel mtight">=</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.311105em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.10903em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.3672129999999998em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8451960000000005em;"><span style="top:-1.8828870000000002em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span><span class="mrel mtight">=</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.316865em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:-0.10903em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.3729729999999998em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">x</span><span class="mopen">[</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">]</span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.1548299999999998em;"><span style="top:-3.50591em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mspace mtight"><span class="mtight"> </span></span><span class="mord mtight">2</span><span class="mord mathnormal mtight" style="margin-right:0.03588em;">π</span><span class="mspace mtight" style="margin-right:0.19516666666666668em;"></span><span class="mop mtight"><span class="mop op-symbol small-op mtight" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9270285714285714em;"><span style="top:-2.1785614285714283em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">0</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.32143857142857146em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.19516666666666668em;"></span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8558428571428572em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3448em;margin-left:-0.10903em;margin-right:0.1em;"><span class="pstrut" style="height:2.65952em;"></span><span class="mord mathnormal mtight">i</span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.31472em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.5483000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3448em;margin-left:-0.03588em;margin-right:0.1em;"><span class="pstrut" style="height:2.65952em;"></span><span class="mord mathnormal mtight">i</span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.31472em;"><span></span></span></span></span></span></span><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3448em;margin-left:0em;margin-right:0.1em;"><span class="pstrut" style="height:2.65952em;"></span><span class="mord mathnormal mtight">i</span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.31472em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.5688em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</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>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">d</span></span></span></span>
</span> = <code class="xref py py-attr docutils literal notranslate"><span class="pre">signal_ndim</span></code> is number of dimensions for the
signal, and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">N_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
</span> is the size of signal dimension <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>
</span>.</p>
<p>This method supports 1D, 2D and 3D complex-to-complex transforms, indicated
by <code class="xref py py-attr docutils literal notranslate"><span class="pre">signal_ndim</span></code>. <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> must be a tensor with last dimension
of size 2, representing the real and imaginary components of complex
numbers, and should have at least <code class="docutils literal notranslate"><span class="pre">signal_ndim</span> <span class="pre">+</span> <span class="pre">1</span></code> dimensions with optionally
arbitrary number of leading batch dimensions. If <code class="xref py py-attr docutils literal notranslate"><span class="pre">normalized</span></code> is set to
<code class="docutils literal notranslate"><span class="pre">True</span></code>, this normalizes the result by dividing it with
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mrow><msubsup><mo>∏</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>K</mi></msubsup><msub><mi>N</mi><mi>i</mi></msub></mrow></msqrt></mrow><annotation encoding="application/x-tex">\sqrt{\prod_{i=1}^K N_i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8399999999999999em;vertical-align:-0.5142395000000001em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3257605em;"><span class="svg-align" style="top:-3.8em;"><span class="pstrut" style="height:3.8em;"></span><span class="mord" style="padding-left:1em;"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∏</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07153em;">K</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.2857605em;"><span class="pstrut" style="height:3.8em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em;"><svg width='400em' height='1.8800000000000001em' viewBox='0 0 400000 1944' preserveAspectRatio='xMinYMin slice'><path d='M983 90
l0 -0
c4,-6.7,10,-10,18,-10 H400000v40
H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7
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</span> so that the operator is unitary.</p>
<p>Returns the real and the imaginary parts together as one tensor of the same
shape of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.</p>
<p>The inverse of this function is <a class="reference internal" href="torch.ifft.html#torch.ifft" title="torch.ifft"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft()</span></code></a>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>For CUDA tensors, an LRU cache is used for cuFFT plans to speed up
repeatedly running FFT methods on tensors of same geometry with same
configuration. See <a class="reference internal" href="../notes/cuda.html#cufft-plan-cache"><span class="std std-ref">cuFFT plan cache</span></a> for more details on how to
monitor and control the cache.</p>
</div>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>If the torch.fft module is imported then “torch.fft” will refer to the
module and not this function. Use <a class="reference internal" href="../tensors.html#torch.Tensor.fft" title="torch.Tensor.fft"><code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.fft()</span></code></a> instead.</p>
</div>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>Due to limited dynamic range of half datatype, performing this operation in half
precision may cause the first element of result to overflow for certain inputs.</p>
</div>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>For CPU tensors, this method is currently only available with MKL. Use
<a class="reference internal" href="../backends.html#torch.backends.mkl.is_available" title="torch.backends.mkl.is_available"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.backends.mkl.is_available()</span></code></a> to check if MKL is installed.</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 of at least <code class="xref py py-attr docutils literal notranslate"><span class="pre">signal_ndim</span></code> <code class="docutils literal notranslate"><span class="pre">+</span> <span class="pre">1</span></code>
dimensions</p></li>
<li><p><strong>signal_ndim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a>) – the number of dimensions in each signal.
<code class="xref py py-attr docutils literal notranslate"><span class="pre">signal_ndim</span></code> can only be 1, 2 or 3</p></li>
<li><p><strong>normalized</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a><em>, </em><em>optional</em>) – controls whether to return normalized results.
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 tensor containing the complex-to-complex Fourier transform result</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>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># unbatched 2D FFT</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">randn</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</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="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">tensor([[[-0.0876, 1.7835],</span>
<span class="go"> [-2.0399, -2.9754],</span>
<span class="go"> [ 4.4773, -5.0119]],</span>
<span class="go"> [[-1.5716, 2.7631],</span>
<span class="go"> [-3.8846, 5.2652],</span>
<span class="go"> [ 0.2046, -0.7088]],</span>
<span class="go"> [[ 1.9938, -0.5901],</span>
<span class="go"> [ 6.5637, 6.4556],</span>
<span class="go"> [ 2.9865, 4.9318]],</span>
<span class="go"> [[ 7.0193, 1.1742],</span>
<span class="go"> [-1.3717, -2.1084],</span>
<span class="go"> [ 2.0289, 2.9357]]])</span>
<span class="gp">>>> </span><span class="c1"># batched 1D FFT</span>
<span class="gp">>>> </span><span class="n">torch</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="mi">1</span><span class="p">)</span>
<span class="go">tensor([[[ 1.8385, 1.2827],</span>
<span class="go"> [-0.1831, 1.6593],</span>
<span class="go"> [ 2.4243, 0.5367]],</span>
<span class="go"> [[-0.9176, -1.5543],</span>
<span class="go"> [-3.9943, -2.9860],</span>
<span class="go"> [ 1.2838, -2.9420]],</span>
<span class="go"> [[-0.8854, -0.6860],</span>
<span class="go"> [ 2.4450, 0.0808],</span>
<span class="go"> [ 1.3076, -0.5768]],</span>
<span class="go"> [[-0.1231, 2.7411],</span>
<span class="go"> [-0.3075, -1.7295],</span>
<span class="go"> [-0.5384, -2.0299]]])</span>
<span class="gp">>>> </span><span class="c1"># arbitrary number of batch dimensions, 2D FFT</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">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="n">torch</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="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span><span class="o">.</span><span class="n">shape</span>
<span class="go">torch.Size([3, 3, 5, 5, 2])</span>
</pre></div>
</div>
</dd></dl>
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