A covariant, discrete time-frequency ...
Type de document :
Article dans une revue scientifique
Titre :
A covariant, discrete time-frequency representation tailored for zero-based signal detection
Auteur(s) :
Pascal, Barbara [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Bardenet, Remi [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Bardenet, Remi [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Titre de la revue :
IEEE Transactions on Signal Processing
Éditeur :
Institute of Electrical and Electronics Engineers
Date de publication :
2022
ISSN :
1053-587X
Mot(s)-clé(s) en anglais :
Time-frequency analysis
Covariant representations
Coherent states
Gaussian Analytic Functions
Spatial statistics
Monte Carlo envelope tests
Covariant representations
Coherent states
Gaussian Analytic Functions
Spatial statistics
Monte Carlo envelope tests
Discipline(s) HAL :
Informatique [cs]/Traitement du signal et de l'image [eess.SP]
Statistiques [stat]/Méthodologie [stat.ME]
Statistiques [stat]/Méthodologie [stat.ME]
Résumé en anglais : [en]
Recent work in time-frequency analysis proposed to switch the focus from the maxima of the spectrogram toward its zeros. The zeros of signals in white Gaussian noise indeed form a random point pattern with a very stable ...
Lire la suite >Recent work in time-frequency analysis proposed to switch the focus from the maxima of the spectrogram toward its zeros. The zeros of signals in white Gaussian noise indeed form a random point pattern with a very stable structure. Using modern spatial statistics tools on the pattern of zeros of a spectrogram has led to component disentanglement and signal detection procedures. The major bottlenecks of this approach are the discretization of the Short-Time Fourier Transform and the necessarily bounded observation window in the time-frequency plane. Both impact the estimation of summary statistics of the zeros, which are then used in standard statistical tests. To circumvent these limitations, we propose a generalized timefrequency representation, which we call the Kravchuk transform. It naturally applies to finite signals, i.e., finite-dimensional vectors. The corresponding phase space, instead of the whole timefrequency plane, is compact, and particularly amenable to spatial statistics. On top of this, the Kravchuk transform has several natural properties for signal processing, among which covariance under the group action of SO(3), invertibility and symmetry with respect to complex conjugation. We further show that the point process of the zeros of the Kravchuk transform of discrete white Gaussian noise coincides in law with the zeros of the spherical Gaussian Analytic Function. This implies that the law of the zeros is invariant under isometries of the sphere. Elaborating on this theorem, we develop a procedure for signal detection based on the spatial statistics of the zeros of the Kravchuk spectrogram. The statistical power of this procedure is assessed by intensive numerical simulation, and compares favorably with respect to state-of-the-art zeros-based detection procedures. Furthermore it appears to be particularly robust to both low signal-to-noise ratio and small number of samples.Lire moins >
Lire la suite >Recent work in time-frequency analysis proposed to switch the focus from the maxima of the spectrogram toward its zeros. The zeros of signals in white Gaussian noise indeed form a random point pattern with a very stable structure. Using modern spatial statistics tools on the pattern of zeros of a spectrogram has led to component disentanglement and signal detection procedures. The major bottlenecks of this approach are the discretization of the Short-Time Fourier Transform and the necessarily bounded observation window in the time-frequency plane. Both impact the estimation of summary statistics of the zeros, which are then used in standard statistical tests. To circumvent these limitations, we propose a generalized timefrequency representation, which we call the Kravchuk transform. It naturally applies to finite signals, i.e., finite-dimensional vectors. The corresponding phase space, instead of the whole timefrequency plane, is compact, and particularly amenable to spatial statistics. On top of this, the Kravchuk transform has several natural properties for signal processing, among which covariance under the group action of SO(3), invertibility and symmetry with respect to complex conjugation. We further show that the point process of the zeros of the Kravchuk transform of discrete white Gaussian noise coincides in law with the zeros of the spherical Gaussian Analytic Function. This implies that the law of the zeros is invariant under isometries of the sphere. Elaborating on this theorem, we develop a procedure for signal detection based on the spatial statistics of the zeros of the Kravchuk spectrogram. The statistical power of this procedure is assessed by intensive numerical simulation, and compares favorably with respect to state-of-the-art zeros-based detection procedures. Furthermore it appears to be particularly robust to both low signal-to-noise ratio and small number of samples.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Projet Européen :
Collections :
Source :
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