Generalized spectrograms and Ï„-Wigner transforms

Boggiatto Paolo; De Donno Giuseppe; Oliaro Alessandro; Bui Kien Cuong

doi:10.4067/S0719-06462010000300011

Authors

Boggiatto Paolo Department of Mathematics, University of Turin, Via Carlo Alberto, 10, 10123 Torino, Italy.
De Donno Giuseppe Department of Mathematics, University of Turin, Via Carlo Alberto, 10, 10123 Torino, Italy.
Oliaro Alessandro Department of Mathematics, University of Turin, Via Carlo Alberto, 10, 10123 Torino, Italy.
Bui Kien Cuong Higher Education Department, Hanoi Pedagogical University 2, Building G7-144 Xuan Thuy Rd – Hanoi, Vietnam.

DOI:

https://doi.org/10.4067/S0719-06462010000300011

Keywords:

Time-Frequency representation, Ï„-Wigner distribution, Generalized spectrogram

Abstract

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