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Being low-rank in the time-frequency plane

Citation Author(s):
Valentin Emiya, Ronan Hamon, Caroline Chaux
Submitted by:
Caroline Chaux
Last updated:
13 April 2018 - 4:18am
Document Type:
Poster
Document Year:
2018
Event:
 

When using optimization methods with matrix variables in signal processing and machine learning, it is customary to assume some low-rank prior on the targeted solution. Nonnegative matrix factorization of spectrograms is a case in point in audio signal processing. However, this low-rank prior is not straightforwardly related to complex matrices obtained from a short-time Fourier -- or discrete Gabor -- transform (STFT), which is generally defined from and studied based on a modulation operator and a translation operator applied to a so-called window. This paper is a first study of the low-rankness property of time-frequency matrices. We characterize the set of signals with a rank-$r$ (complex) STFT matrix in the case of a unit hop size and frequency step with few assumptions on the transform parameters. We discuss the scope of this result and its implications on low-rank approximations of STFT matrices.

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