Title :

A Generalization of the Fourier Transform and its Application to Spectral Analysis of Chirp-like Signals

Author(s) :

Mboup, Mamadou [Auteur]
Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804 [CRESTIC]
Non-Asymptotic estimation for online systems [NON-A]
Adali, Tülay [Auteur]

Journal title :

Applied and Computational Harmonic Analysis

Publisher :

Elsevier

Publication date :

2011

ISSN :

1063-5203

English keyword(s) :

de Branges spaces
Fourier transform
Chirps
Reproducing kernel

HAL domain(s) :

Informatique [cs]/Traitement du signal et de l'image [eess.SP]
Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]

English abstract : [en]

We show that the de Branges theory provides a useful generalization of the Fourier Transform (FT). The formulation is quite rich in that by selecting the appropriate para\-me\-trization, one can obtain spectral representation ...
Show more >We show that the de Branges theory provides a useful generalization of the Fourier Transform (FT). The formulation is quite rich in that by selecting the appropriate para\-me\-trization, one can obtain spectral representation for a number of important cases. We demonstrate two such cases in this paper: the finite sum of elementary chirp-like signals, and a decaying chirp using Bessel functions. We show that when defined in the framework of de Branges spaces, these cases admit a representation very much similar to the spectral representation of a finite sum of sinusoids for the usual FT.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL