Filterbank in Tensorflow and Pytorch

Background

Short-time Fourier transform (STFT) is still widely used for time-frequency analysis. However, filter banks are far more flexible and performant with little extra computational complexity.

Types of filter banks and their prototype filter designs

Filter banks with efficient implementations always use periodic modulation sequences and FFT like fast algorithms. There are plenty of design examples here. A discrete Fourier transform (DFT) modulated prototype design example is included here for demo purpose.

View of overlapping chunks of the time domain signal

This operation is required for analysis. It corresponds to numpy.lib.stride_tricks.as_strided in Numpy, tf.signal.frame in Tensorflow, and torch.nn.functional.unfold in Pytorch.

Overlap-and-add

This operation is required for synthesis. It corresponds to tf.signal.overlap_and_add in Tensorflow, and torch.nn.functional.fold in Pytorch. Seems that numpy/scipy does not provide a native vectorized overlap-and-add implementation.

Implementations in this package

I have implemented the DFT modulated filter bank for real-valued signals. The filter length is assumed to be a multiple of FFT length so that no zero padding is needed for vectorized implementation. Implementations for complex-valued signals and/or other modulations like DCT-IV should be similar.