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<div class="section" id="torch-istft">
<h1>torch.istft<a class="headerlink" href="#torch-istft" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.istft">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">istft</code><span class="sig-paren">(</span><em class="sig-param">input: torch.Tensor</em>, <em class="sig-param">n_fft: int</em>, <em class="sig-param">hop_length: Optional[int] = None</em>, <em class="sig-param">win_length: Optional[int] = None</em>, <em class="sig-param">window: Optional[torch.Tensor] = None</em>, <em class="sig-param">center: bool = True</em>, <em class="sig-param">normalized: bool = False</em>, <em class="sig-param">onesided: Optional[bool] = None</em>, <em class="sig-param">length: Optional[int] = None</em>, <em class="sig-param">return_complex: bool = False</em><span class="sig-paren">)</span> → torch.Tensor<a class="reference internal" href="../_modules/torch/functional.html#istft"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.istft" title="Permalink to this definition">¶</a></dt>
<dd><p>Inverse short time Fourier Transform. This is expected to be the inverse of <a class="reference internal" href="torch.stft.html#torch.stft" title="torch.stft"><code class="xref py py-func docutils literal notranslate"><span class="pre">stft()</span></code></a>.
It has the same parameters (+ additional optional parameter of <code class="xref py py-attr docutils literal notranslate"><span class="pre">length</span></code>) and it should return the
least squares estimation of the original signal. The algorithm will check using the NOLA condition (
nonzero overlap).</p>
<p>Important consideration in the parameters <code class="xref py py-attr docutils literal notranslate"><span class="pre">window</span></code> and <code class="xref py py-attr docutils literal notranslate"><span class="pre">center</span></code> so that the envelop
created by the summation of all the windows is never zero at certain point in time. Specifically,
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mo>−</mo><mi mathvariant="normal">∞</mi></mrow><mi mathvariant="normal">∞</mi></msubsup><mi mathvariant="normal">∣</mi><mi>w</mi><msup><mi mathvariant="normal">∣</mi><mn>2</mn></msup><mo stretchy="false">[</mo><mi>n</mi><mo>−</mo><mi>t</mi><mo>×</mo><mi>h</mi><mi>o</mi><mi>p</mi><mi mathvariant="normal">_</mi><mi>l</mi><mi>e</mi><mi>n</mi><mi>g</mi><mi>t</mi><mi>h</mi><mo stretchy="false">]</mo><menclose notation="updiagonalstrike"><mo lspace="0em" rspace="0em">=</mo></menclose><mn>0</mn></mrow><annotation encoding="application/x-tex">\sum_{t=-\infty}^{\infty} |w|^2[n-t\times hop\_length] \cancel{=} 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.172149em;vertical-align:-0.35804100000000005em;"></span><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:0.804292em;"><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">t</span><span class="mrel mtight">=</span><span class="mord mtight">−</span><span class="mord mtight">∞</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 mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.35804100000000005em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord"><span class="mord">∣</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen">[</span><span class="mord mathnormal">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><span class="base"><span class="strut" style="height:0.69841em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">t</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:1.06em;vertical-align:-0.31em;"></span><span class="mord mathnormal">h</span><span class="mord mathnormal">o</span><span class="mord mathnormal">p</span><span class="mord" style="margin-right:0.02778em;">_</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mclose">]</span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.56687em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mrel">=</span></span></span><span class="svg-align" style="top:-2.8em;"><span class="pstrut" style="height:3em;"></span><span style="height:0.7668699999999999em;"><svg width='100%' height='0.7668699999999999em'><line x1='0' y1='100%' x2='100%' y2='0' stroke-width='0.046em'/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2em;"><span></span></span></span></span></span><span class="mord">0</span></span></span></span>
</span>.</p>
<p>Since <a class="reference internal" href="torch.stft.html#torch.stft" title="torch.stft"><code class="xref py py-func docutils literal notranslate"><span class="pre">stft()</span></code></a> discards elements at the end of the signal if they do not fit in a frame,
<code class="docutils literal notranslate"><span class="pre">istft</span></code> may return a shorter signal than the original signal (can occur if <code class="xref py py-attr docutils literal notranslate"><span class="pre">center</span></code> is False
since the signal isn’t padded).</p>
<p>If <code class="xref py py-attr docutils literal notranslate"><span class="pre">center</span></code> is <code class="docutils literal notranslate"><span class="pre">True</span></code>, then there will be padding e.g. <code class="docutils literal notranslate"><span class="pre">'constant'</span></code>, <code class="docutils literal notranslate"><span class="pre">'reflect'</span></code>, etc.
Left padding can be trimmed off exactly because they can be calculated but right padding cannot be
calculated without additional information.</p>
<p>Example: Suppose the last window is:
<code class="docutils literal notranslate"><span class="pre">[17,</span> <span class="pre">18,</span> <span class="pre">0,</span> <span class="pre">0,</span> <span class="pre">0]</span></code> vs <code class="docutils literal notranslate"><span class="pre">[18,</span> <span class="pre">0,</span> <span class="pre">0,</span> <span class="pre">0,</span> <span class="pre">0]</span></code></p>
<p>The <code class="xref py py-attr docutils literal notranslate"><span class="pre">n_fft</span></code>, <code class="xref py py-attr docutils literal notranslate"><span class="pre">hop_length</span></code>, <code class="xref py py-attr docutils literal notranslate"><span class="pre">win_length</span></code> are all the same which prevents the calculation
of right padding. These additional values could be zeros or a reflection of the signal so providing
<code class="xref py py-attr docutils literal notranslate"><span class="pre">length</span></code> could be useful. If <code class="xref py py-attr docutils literal notranslate"><span class="pre">length</span></code> is <code class="docutils literal notranslate"><span class="pre">None</span></code> then padding will be aggressively removed
(some loss of signal).</p>
<p>[1] D. W. Griffin and J. S. Lim, “Signal estimation from modified short-time Fourier transform,”
IEEE Trans. ASSP, vol.32, no.2, pp.236-243, Apr. 1984.</p>
<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. Expected to be output of <a class="reference internal" href="torch.stft.html#torch.stft" title="torch.stft"><code class="xref py py-func docutils literal notranslate"><span class="pre">stft()</span></code></a>,
can either be complex (<code class="docutils literal notranslate"><span class="pre">channel</span></code>, <code class="docutils literal notranslate"><span class="pre">fft_size</span></code>, <code class="docutils literal notranslate"><span class="pre">n_frame</span></code>), or real
(<code class="docutils literal notranslate"><span class="pre">channel</span></code>, <code class="docutils literal notranslate"><span class="pre">fft_size</span></code>, <code class="docutils literal notranslate"><span class="pre">n_frame</span></code>, 2) where the <code class="docutils literal notranslate"><span class="pre">channel</span></code>
dimension is optional.</p></li>
<li><p><strong>n_fft</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a>) – Size of Fourier transform</p></li>
<li><p><strong>hop_length</strong> (<em>Optional</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em>) – The distance between neighboring sliding window frames.
(Default: <code class="docutils literal notranslate"><span class="pre">n_fft</span> <span class="pre">//</span> <span class="pre">4</span></code>)</p></li>
<li><p><strong>win_length</strong> (<em>Optional</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em>) – The size of window frame and STFT filter. (Default: <code class="docutils literal notranslate"><span class="pre">n_fft</span></code>)</p></li>
<li><p><strong>window</strong> (<em>Optional</em><em>[</em><a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>torch.Tensor</em></a><em>]</em>) – The optional window function.
(Default: <code class="docutils literal notranslate"><span class="pre">torch.ones(win_length)</span></code>)</p></li>
<li><p><strong>center</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a>) – Whether <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> was padded on both sides so that the <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord mathnormal">t</span></span></span></span>
</span>-th frame is
centered at time <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mo>×</mo><mtext>hop_length</mtext></mrow><annotation encoding="application/x-tex">t \times \text{hop\_length}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69841em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">t</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:1.00444em;vertical-align:-0.31em;"></span><span class="mord text"><span class="mord">hop_length</span></span></span></span></span>
</span>.
(Default: <code class="docutils literal notranslate"><span class="pre">True</span></code>)</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>) – Whether the STFT was normalized. (Default: <code class="docutils literal notranslate"><span class="pre">False</span></code>)</p></li>
<li><p><strong>onesided</strong> (<em>Optional</em><em>[</em><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>) – Whether the STFT was onesided.
(Default: <code class="docutils literal notranslate"><span class="pre">True</span></code> if <code class="docutils literal notranslate"><span class="pre">n_fft</span> <span class="pre">!=</span> <span class="pre">fft_size</span></code> in the input size)</p></li>
<li><p><strong>length</strong> (<em>Optional</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em>) – The amount to trim the signal by (i.e. the
original signal length). (Default: whole signal)</p></li>
<li><p><strong>return_complex</strong> (<em>Optional</em><em>[</em><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>) – Whether the output should be complex, or if the input should be
assumed to derive from a real signal and window.
Note that this is incompatible with <code class="docutils literal notranslate"><span class="pre">onesided=True</span></code>.
(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>Least squares estimation of the original signal of size (…, signal_length)</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>
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