Complex support for stft and istft (#43886)
Summary:
Ref https://github.com/pytorch/pytorch/issues/42175, fixes https://github.com/pytorch/pytorch/issues/34797
This adds complex support to `torch.stft` and `torch.istft`. Note that there are really two issues with complex here: complex signals, and returning complex tensors.
## Complex signals and windows
`stft` currently assumes all signals are real and uses `rfft` with `onesided=True` by default. Similarly, `istft` always takes a complex fourier series and uses `irfft` to return real signals.
For `stft`, I now allow complex inputs and windows by calling the full `fft` if either are complex. If the user gives `onesided=True` and the signal is complex, then this doesn't work and raises an error instead. For `istft`, there's no way to automatically know what to do when `onesided=False` because that could either be a redundant representation of a real signal or a complex signal. So there, the user needs to pass the argument `return_complex=True` in order to use `ifft` and get a complex result back.
## stft returning complex tensors
The other issue is that `stft` returns a complex result, represented as a `(... X 2)` real tensor. I think ideally we want this to return proper complex tensors but to preserver BC I've had to add a `return_complex` argument to manage this transition. `return_complex` defaults to false for real inputs to preserve BC but defaults to True for complex inputs where there is no BC to consider.
In order to `return_complex` by default everywhere without a sudden BC-breaking change, a simple transition plan could be:
1. introduce `return_complex`, defaulted to false when BC is an issue but giving a warning. (this PR)
2. raise an error in cases where `return_complex` defaults to false, making it a required argument.
3. change `return_complex` default to true in all cases.
Pull Request resolved: https://github.com/pytorch/pytorch/pull/43886
Reviewed By: glaringlee
Differential Revision: D23760174
Pulled By: mruberry
fbshipit-source-id: 2fec4404f5d980ddd6bdd941a63852a555eb9147
