Generalization of the Choi-Williams Distribution and the Butterworth Distribution for Time-Frequency Analysis
We provide a generalization to the Choi-Williams expo- nential distribution and introduce the new Butterworth distribution. We compute design equations and curves for the optimal choices of their parameters and for the optimal value of c of the exponential dis- tribution. We also provide examples that demonstrate the superior performance of our method over the Choi-Williams. Our new distri- butions can achieve cross-term reduction and autoterm preservation simultaneously, whereas the Choi-Williams distribution suffers from an inherent tradeoff between the two.