A mixed time-frequency-scale analysis of the hybrid wavefront-resonance representation

Several time-frequency-scale processing schemes for the analysis of short pulse scattering fields are explored and calibrated in connection with the problem of reflections from multilayered dispersive media. The time-frequency signature consists of a (generally nonuniform) grid of wavefront arrivals and resonances. It is shown that the time-frequency resolution is bound by the unit-cell area, hence the signature of a particular wave process can be detected only if the processing windows are scale-matched to corresponding unit cells. The short-time Fourier transform (STFT) has therefore an inherent limitation because it has a built in scale, while the wavelet transform with a Morlet wavelet provides a framework that adapts to all scales with no a-priori information while retaining the frequency signature of the resonances. Localized scrutiny of a specific scale may then be achieved using the STFT, while super resolution may be achieved using a model based analysis.