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DEMO_FILTERBANKSYNCHROSQUEEZE - Filterbank synchrosqueezing and inversion

Description

The demo shows that the synchrosqueezed filterbank representation can be directly used to reconstruct the original signal. Since we do not work with a filterbank which forms a tight frame (its filterbankresponse is not constant) the direct reconstruction (mere summing all the channels) does not work well. We can fix that by filtering (equalizing) the result by the inverse of the overall analysis filterbank frequency response.

demo_filterbanksynchrosqueeze_1.png

ERBlet spectrogram (top) and synchrosqueezed ERBlet spectrogram (bottom)

The signal used is the first second from gspi. Only the energy of the coefficients is show. Both representations are in fact complex and invertible.
demo_filterbanksynchrosqueeze_2.png

Errors of the direct and the equalized reconstructions

There is still a small DC offset of the signal obtained by the direct summation.

References:

N. Holighaus, Z. Průša, and P. L. Søndergaard. Reassignment and synchrosqueezing for general time-frequency filter banks, subsampling and processing. Signal Processing, 125:1--8, 2016. [ DOI | http ]