We consider in this paper Wigner type representations Wig t 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 Wig t with a tempered distribution. We introduce furthermore a class of quadratic representations Sp t based on the t-Wigner, as an extension of the two window Spectrogram (see [2]). We give basic properties of Sp t as subclasses of the general Cohen class.