Hybrid linear/bilinear time-scale analysis

We introduce a new method for the time-scale analysis of nonstationary signals. Our work leverages the success of the "time-frequency distribution series/cross-term deleted representations" into the time-scale domain to match wideband 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 timescale 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.