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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.3 Temuco  2010

http://dx.doi.org/10.4067/S0719-06462010000300011 

CUBO A Mathematical Journal Vol.12, N° 03, (171–185). October 2010

 

Generalized Spectrograms and t -Wigner Transforms

 

BOGGIATTO PAOLO, DE DONNO GIUSEPPE, OLIARO ALESSANDRO AND BUI KIEN CUONG

Department of Mathematics, University of Turin, Via Carlo Alberto, 10, 10123 Torino, Italy email: paolo.boggiatto@unito.it email: giuseppe.dedonno@unito.it, email: alessandro.oliaro@unito.it

Higher Education Department, Hanoi Pedagogical University 2, Building G7-144 Xuan Thuy Rd – Hanoi, Vietnam email: buikiencuong@yahoo.com


ABSTRACT

We consider in this paper Wigner type representations Wigt depending on a parameter t ∈ [0,1] as defined in [2]. We prove that the Cohen class can be characterized in terms of the convolution of such Wigt with a tempered distribution. We introduce furthermore a class of “quadratic representations” Spt based on the t-Wigner, as an extension of the two window Spectrogram (see [2]). We give basic properties of Spt as subclasses of the general Cohen class.

Key words and phrases: Time-Frequency representation, t-Wigner distribution, generalized Spectrogram.


RESUMEN

Nosotros consideramos en este artículo representaciones de tipoWigner Wigt dependiendo de um parámetro t ∈ [0,1] como definido en [2]. Probamos que la clase Cohen puede ser caracterizada en terminos de la convolución de tales Wigt con una distribución temperada. Introducimos también la clase de “representaciones cuadraticas” Spt basado en el t-Wigner, como una extensión de dos ventanas espectrograma (ver [2]). Nosotros damos propiedades básicas de Spt como subclases de la clase Cohen.

Math. Subj. Class.: 42B10, 47A07, 33C05.


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