Ridges associated to continuous linear time-frequency representations of asymptotic and transient signals

In most fields of experimental physics, signals to be considered possess evolutive spectral characteristics. This situation is encountered for instance when one deals with acoustic signals, from musical sounds to nondestructive evaluation (Guillemain and Kronland-Martinet, 1996). The characterization of such signals is improved if time-frequency techniques are used. The representations obtained this way lead to a qualitative description of the signals and suffer of internal constraints that can introduce a kind of missunderstanding. In this paper, we shall briefly present techniques allowing a quantitative description of signals being a sum of amplitude and frequency modulated components. We shall only consider here monocomponent signals, the generalization to multicomponent signals as well as the algorithmic aspects being given previously (Guillemain and Kronland-Martinet, 1996).