Generalized spectrograms and Ï„-Wigner transforms

Abstract

We consider in this paper Wigner type representations Wig_Ï„ depending on a parameter Ï„ ∈ [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.