Characterization of finite signals with low-rank STFT

Konstantin Usevich (1) , Valentin Emiya (2) , David Brie (1) , Caroline Chaux (3)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 QARMA - éQuipe d'AppRentissage de MArseille
3 I2M - Institut de Mathématiques de Marseille

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 comprehensive answer in case of maximal overlap, where the class of signals includes products of complex exponentials and polynomials. In the general case, other exotic examples may appear.

Mots clés: low-rank approximation; Hankel matrices; Short-time Fourier transform

Domaines: Traitement du signal et de l'image [eess.SP]

Konstantin Usevich, Valentin Emiya, David Brie, Caroline Chaux. Characterization of finite signals with low-rank STFT. IEEE Statistical Signal Processing Workshop (SSP), Jun 2018, Freiburg, Germany. ⟨hal-01717931v1⟩