I'm trying to implement this paper in tensorflow and keras. At the end of section 3 it says.

Note that although weighted SDR loss is a time-domain loss function,
it can be backpropagated through our framework.
Specifically, STFT and ISTFT operations are implemented as 1-D convolution
and deconvolution layers consisting of fixed filters initialized 
with the discrete Fourier transform matrix.

How would I go about implementing an STFT and an ISTFT as a 1-D convolution and 1-D deconvolution respectively? For example how would the window size and the hop length correspond to parameters of a convolution?

Conversely, could I just use tensorflow's built in STFT and inverse_STFT ops instead?


I found an implementation of STFT based on conv1d in pytorch here:


edit: Actually, the phasen repository took the STFT code from https://github.com/pseeth/torch-stft edit2: Asteroid has an alternative implementation of STFT and iSTFT: https://github.com/mpariente/asteroid/


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