Short-time Fourier transform (STFT) and inverse short-time Fourier transform (ISTFT) in python.

This module is based on the algorithm proposed in [1]. The features of this module include

• the input data is assumed to be real (use rfft/irfft instead of fft/ifft)
• it can be applied to an n-d array
• the segmentation is always along the first dimension
• overlapping segments are allowed
• zero padding is allowed
• the ISTFT can be performed using overlap-and-add (p=1) or a least squares approach (p=2).
• This module can be dropped into your project. Scipy also includes an stft/istft implementation.

Additional works that use this stft/istft approach include [2-5].

If you use this code in work that you publish, please consider citing at least one of [2-5].

[1] B Yang, "A study of inverse short-time Fourier transform," in Proc. of ICASSP, 2008.

[2] B Byram et al, "Ultrasonic multipath and beamforming clutter reduction: a chirp model approach," IEEE UFFC, 61, 3, 2014.

[3] B Byram et al, "A model and regularization scheme for ultrasonic beamforming clutter reduction, " IEEE UFFC, 62, 11, 2015.

[4] A Luchies and B Byram, "Deep neural networks for ultrasound beamforming," IEEE TMI, 37, 9, 2018.

[5] A Luchies and B Byram, "Training improvements for ultrasound beamforming with deep neural networks," PMB, 64, 4, 2019.