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Generalization of the Choi-Williams Distribution and the Butterworth Distribution for Time-Frequency Analysis

We provide a generalization to the Choi-Williams exponential 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 distribution. We also provide examples that demonstrate the superior performance of our method over the Choi-Williams. Our new distributions can achieve cross-term reduction and autoterm preservation simultaneously, whereas the Choi-Williams distribution suffers from an inherent tradeoff between the two.