A Generalization of the Fourier Transform ...
Document type :
Article dans une revue scientifique: Article original
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]
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
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]
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 >
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 :
Source :
Files
- https://hal.inria.fr/hal-00640508v2/document
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- https://hal.inria.fr/hal-00640508v2/document
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- https://hal.inria.fr/hal-00640508v2/document
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- https://hal.inria.fr/hal-00640508v2/document
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- https://doi.org/10.1016/j.acha.2011.11.002
- Open access
- Access the document
- document
- Open access
- Access the document
- debranges_chirp_ACHA_HAL.pdf
- Open access
- Access the document
- j.acha.2011.11.002
- Open access
- Access the document