On the Statistics of Spectrogram Reassignment Vectors

Chassande–Mottin, E.; Flandrin, Patrick; Auger, François

doi:10.1007/978-1-4757-2838-5_3

Cited by 5 publications

(3 citation statements)

References 3 publications

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“…Another important topic in the study of SSTs is the statistical analysis of the synchrosqueezing operator, since noise is ubiquitous in real applications. A pioneer paper [10] in this direction studied the statistical properties of the 1D spectrogram reassignment method by calculating the probability density function of white Gaussian noise after reassignment. A recent paper [36] focused on the statistical analysis of the 1D SSWT for white Gaussian noise.…”

Section: Introductionmentioning

confidence: 99%

Statistical analysis of synchrosqueezed transforms

Yang

2018

Applied and Computational Harmonic Analysis

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Synchrosqueezed transforms are non-linear processes for a sharpened time-frequency representation of wave-like components. They are efficient tools for identifying and analyzing wave-like components from their superposition. This paper is concerned with the statistical properties of compactly supported synchrosqueezed transforms for wave-like components embedded in a generalized Gaussian random process in multidimensional spaces. Guided by the theoretical analysis of these properties, new numerical implementations are proposed to reduce the noise fluctuations of these transforms on noisy data. A MATLAB package SynLab together with several heavily noisy examples is provided to support these theoretical claims.

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Section: Introductionmentioning

confidence: 99%

Statistical analysis of synchrosqueezed transforms

Yang

2018

Applied and Computational Harmonic Analysis

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“…Some interesting results for the phase derivative have been shown in the context of reassignment. In [8], the following result is given: We consider a zero-mean Gaussian analytic white noise f such that…”

Section: Numerical Observationsmentioning

confidence: 99%

The pole behavior of the phase derivative of the short-time Fourier transform

Balázs

Bayer

Jaillet

et al. 2016

Applied and Computational Harmonic Analysis

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Abstract. The short-time Fourier transform (STFT) is a timefrequency representation widely used in applications, for example in audio signal processing. Recently it has been shown that not only the amplitude, but also the phase of this representation can be successfully exploited for improved analysis and processing. In this paper we describe a rather peculiar pole phenomenon in the phase derivative, a recurring pattern that appears in a characteristic way in the neighborhood around any of the zeros of the STFT, a negative peak followed by a positive one. We describe this phenomenon numerically and provide a complete analytical explanation.

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“…[4] showed that some Cohen's group TFRs can be used to implement optimal linear detection, by providing an equivalent implementation of the time domain matched filter in the time frequency domain. This seminal work was followed by a number of studies about time-frequency detection / classification of signals, see e.g., [5]- [8]. All these approaches rely on the idea that the noise is spread all over the timefrequency plane, thus increasing the local signal-to-noise ratio.…”

Section: Introduction a Backgroundmentioning

confidence: 99%