Hybrid linear/bilinear time-scale analysis

We introduce a new method for the time-scale analysis of non-stationary signals. Our work leverages the success of the “time-frequency distribution series / cross-term deleted representations” into the time-scale domain to match wide-band signals that are better modeled in terms of time shifts and scale changes than in terms of time and frequency shifts. Using a wavelet decomposition and the Bertrand time-scale distribution, we locally balance linearity and bilinearity in order to provide good resolution while suppressing troublesome interference components. The theory of frames provides a unifying perspective for cross-term deleted representations in general. This work was supported by the National Science Foundation, grant no. MIP–9457438, and the Office of Naval Research, grant no. N00014–95–1–0849. 1