We consider in this paper Wigner type representations $\Wig_\tau$ depending on a parameter $\tau\in[0,1]$. We prove that the Cohen class can be characterized in terms of the convolution of such $\Wig_\tau$ with a tempered distribution. We introduce furthermore a class of ``quadratic representations'' $\Sp^{\tau}$ based on the $\tau$-Wigner, as an extension of the two window Spectrogram. We give basic properties of $\Sp^{\tau}$ as subclasses of the general Cohen class.
Generalized Spectrograms and $\tau$-Wigner Transforms
BOGGIATTO, Paolo;DE DONNO, Giuseppe;OLIARO, Alessandro
2010-01-01
Abstract
We consider in this paper Wigner type representations $\Wig_\tau$ depending on a parameter $\tau\in[0,1]$. We prove that the Cohen class can be characterized in terms of the convolution of such $\Wig_\tau$ with a tempered distribution. We introduce furthermore a class of ``quadratic representations'' $\Sp^{\tau}$ based on the $\tau$-Wigner, as an extension of the two window Spectrogram. We give basic properties of $\Sp^{\tau}$ as subclasses of the general Cohen class.
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