On a generalization of the Choi-Williams time-frequency distribution

The authors propose a generalization of the kernel of the Choi-Williams time-frequency exponential distribution (ED). The generalized ED (GED) has a lowpass kernel with a variable, flatter passband and a narrower transition region than the ED. As a result, it reduces more low frequency cross-terms than the ED and provides less auto-term distortion, while simultaneously maintaining the desirable time-frequency representation properties of the ED. Given a set of passband and stopband constraints, optimal design equations are provided for the GED parameters as well as the ED scaling parameter