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 wide-band signals that are not well modeled in terms of time and frequency shifts. Using a wavelet decomposition and the Bertrand (see J. Math. Phys., vol.33, p.2515-27, 1992) 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 and leads us to insights into the cross-term deleted representations.