Joint fractional representations

By using Cohen's (1995) characteristic function operator method, we derive the formulation of joint fractional representations (JFRs). JFRs generalize conventional time-frequency representations into fractional domains which are defined by the fractional Fourier transform. We present some of the properties of the fractional Wigner distribution along with the properties of the fractional ambiguity function. We calculate fractional Wigner distributions of some signals and provide some examples.