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Conference Papers Year : 2018

Being low-rank in the time-frequency plane

Valentin Emiya
Ronan Hamon
Caroline Chaux

Abstract

When solving inverse problems and 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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Dates and versions

hal-01636111 , version 1 (16-11-2017)

Identifiers

  • HAL Id : hal-01636111 , version 1

Cite

Valentin Emiya, Ronan Hamon, Caroline Chaux. Being low-rank in the time-frequency plane. ICASSP - IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2018, Calgary, Canada. ⟨hal-01636111⟩
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