New concepts in narrowband and wideband Weyl correspondence time-frequency techniques

We propose the new P₀-Weyl symbol to analyze system induced time shifts and scale changes on the input signal. This new Weyl symbol (WS) is useful in wideband signal analysis. We also propose new WS as tools for analyzing systems which produce dispersive frequency shifts on the signal. We obtain these generalized, frequency-shift covariant WS by warping conventional, narrowband WS. Using the new, generalized WS, we provide a formulation for the Weyl correspondence for linear systems with instantaneous frequency characteristics matched to user specified characteristics. We also propose a new interpretation of linear signal transformations as weighted superpositions of nonlinear frequency shifts on the signal. Application examples in signal analysis and detection demonstrate the advantages of our new results