Characterization of finite signals with low-rank STFT

Abstract : The goal of this paper is characterize finite-length signals that have a low-rank short-time Fourier transform. By using the connection with Hankel matrices, we give a complete answer for maximal overlap, where the class of signals includes products of complex exponentials and polynomials. For the general case, we show that such signals are much more diverse.
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Konstantin Usevich, Valentin Emiya, David Brie, Caroline Chaux. Characterization of finite signals with low-rank STFT. IEEE Statistical Signal Processing Workshop, SSP 2018, Jun 2018, Freiburg, Germany. ⟨10.1109/SSP.2018.8450745⟩. ⟨hal-01717931v2⟩

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