A wideband time-frequency Weyl symbol and its generalization

We extend the work of Shenoy and Parks (1994) on the wideband Weyl correspondence. We define a wideband Weyl symbol (P₀WS) in the time-frequency plane based on the Bertrand (1988) P₀-distribution, and we study its properties, examples and possible applications. Using warping relations, we generalize the P₀WS and the wideband spreading function (WSF) to analyze systems producing dispersive time shifts. We provide properties and special cases (e.g. power and exponential) to demonstrate the importance of our generalization. The new generalized WSF provides a new interpretation of a system output as a weighted superposition of dispersive time-shifted versions of the signal. We provide application examples in analysis and detection to demonstrate the advantages of our new results for linear systems with group delay characteristics matched to the specific warping used