Asymptotic wavelet and Gabor analysis: Extraction of instantaneous frequencies

We investigate the behaviour of the continuous wavelet and Gabor coefficients in the asymptotic limit, using stationary phase approximations. In particular, we show how, under some additional assumptions, these coefficients allow the extraction of some characteristics of the analysed signal, like for example frequency and amplitude modulation laws. We also briefly discuss applications to spectral lines estimations and matched filtering.