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