torch.istft

torch.istft(input, n_fft, hop_length=None, win_length=None, window=None, center=True, normalized=False, onesided=None, length=None, return_complex=False) → Tensor:

Inverse short time Fourier Transform. This is expected to be the inverse of stft().

It has the same parameters (+ additional optional parameter of length) and it should return the least squares estimation of the original signal. The algorithm will check using the NOLA condition ( nonzero overlap).

Important consideration in the parameters window and center so that the envelop created by the summation of all the windows is never zero at certain point in time. Specifically, $\sum_{t=-\infty}^{\infty} |w|^2[n-t\times hop\_length] \cancel{=} 0$.

Since stft() discards elements at the end of the signal if they do not fit in a frame, istft may return a shorter signal than the original signal (can occur if center is False since the signal isn’t padded). If length is given in the arguments and is longer than expected, istft will pad zeros to the end of the returned signal.

If center is True, then there will be padding e.g. 'constant', 'reflect', etc. Left padding can be trimmed off exactly because they can be calculated but right padding cannot be calculated without additional information.

Example: Suppose the last window is: [17, 18, 0, 0, 0] vs [18, 0, 0, 0, 0]

The n_fft, hop_length, win_length 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 length could be useful. If length is None then padding will be aggressively removed (some loss of signal).

[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.

Parameters

• input (Tensor) –

  The input tensor. Expected to be in the format of stft(), output. That is a complex tensor of shape (B?, N, T) where

  • B? is an optional batch dimension
  • N is the number of frequency samples, (n_fft // 2) + 1 for onesided input, or otherwise n_fft.
  • T is the number of frames, 1 + length // hop_length for centered stft, or 1 + (length - n_fft) // hop_length otherwise.

  Changed in version 2.0: Real datatype inputs are no longer supported. Input must now have a complex datatype, as returned by stft(..., return_complex=True).

• n_fft (int) – Size of Fourier transform
• hop_length (Optional[int]) – The distance between neighboring sliding window frames. (Default: n_fft // 4)
• win_length (Optional[int]) – The size of window frame and STFT filter. (Default: n_fft)
• window (Optional[torch.Tensor]) – The optional window function. Shape must be 1d and <= n_fft (Default: torch.ones(win_length))
• center (bool) – Whether input was padded on both sides so that the $t$-th frame is centered at time $t \times \text{hop\_length}$. (Default: True)
• normalized (bool) – Whether the STFT was normalized. (Default: False)
• onesided (Optional[bool]) – Whether the STFT was onesided. (Default: True if n_fft != fft_size in the input size)
• length (Optional[int]) – The amount to trim the signal by (i.e. the original signal length). Defaults to (T - 1) * hop_length for centered stft, or n_fft + (T - 1) * hop_length otherwise, where T is the number of input frames.
• return_complex (Optional[bool]) – 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 onesided=True. (Default: False)

Returns

Least squares estimation of the original signal of shape (B?, length) where

B? is an optional batch dimension from the input tensor.

Return type

Tensor