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yn- opened this issue May 14, 2025 · 0 comments
Open

Documentation: A possible mistake in the STFT formula #153531

yn- opened this issue May 14, 2025 · 0 comments
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module: docs Related to our documentation, both in docs/ and docblocks module: fft triaged This issue has been looked at a team member, and triaged and prioritized into an appropriate module

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@yn-
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yn- commented May 14, 2025 •
edited by pytorch-bot bot
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📚 The doc issue

In the stft documentation, the formula is given as follows:

pytorch/torch/functional.py

Lines 598 to 601 in 1341794

.. math::
X[\omega, m] = \sum_{k = 0}^{\text{win\_length-1}}%
\text{window}[k]\ \text{input}[m \times \text{hop\_length} + k]\ %
\exp\left(- j \frac{2 \pi \cdot \omega k}{\text{n\_fft}}\right),

$$X[\omega, m] = \sum_{k = 0}^{\text{win}\textunderscore\text{length-1}}% \text{window}[k]\ \text{input}[m \times \text{hop}\textunderscore\text{length} + k]\ % \exp\left(- j \frac{2 \pi \cdot \omega k}{\text{n}\textunderscore\text{fft}}\right),$$

The denominator in the exponent is n_fft. Is that a mistake? I would expect the window length here rather than the number of frequency samples. I cannot find the actual implementation by a quick lookaround, so I have not checked what is done by the code.

Apart from the above, a minor issue is that the '- 1' on top of the sum sign should be outside of the \text macro.

Suggest a potential alternative/fix

Change the denominator to win_length, and leave '-1' in math mode.

     .. math:: 
         X[\omega, m] = \sum_{k = 0}^{\text{win\_length}-1}% 
                             \text{window}[k]\ \text{input}[m \times \text{hop\_length} + k]\ % 
                             \exp\left(- j \frac{2 \pi \cdot \omega k}{\text{win\_length}}\right),

$$X[\omega, m] = \sum_{k = 0}^{\text{win}\textunderscore\text{length}-1}% \text{window}[k]\ \text{input}[m \times \text{hop}\textunderscore\text{length} + k]\ % \exp\left(- j \frac{2 \pi \cdot \omega k}{\text{win}\textunderscore\text{length}}\right),$$

cc @svekars @sekyondaMeta @AlannaBurke @mruberry
@yn- yn- changed the title A possible mistake in the STFT formula Documentation: A possible mistake in the STFT formula May 14, 2025
@soulitzer soulitzer added triaged This issue has been looked at a team member, and triaged and prioritized into an appropriate module module: fft module: docs Related to our documentation, both in docs/ and docblocks labels May 14, 2025
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