Analysis of time-varying signals with small BT values

We compare four different methods for analyzing time-varying signals, the frequency and amplitude of which are both varying (small BT signals, where B is the bandwidth and T the duration). All four methods give results which depend on the frequency bandwidth of the analyzing filter. But the modified moving window method (MMWM) (Kodera et al. [10]) is the one which gives the most significant result whatever the value of the filtering bandwidth. This is demonstrated both by a mathematical treatment and by a numerical simulation. In general, there are two characteristic curves in the frequency-time plane: one which gives the instantaneous frequency as a function of time and the other which gives the group delay time as a function of frequency. For signals with small BT values, these two curves are distinct and the different analyzing methods approach one or the other curve, or neither of them, depending on the bandwidth of the filtering window. The ability of each method to resolve multicomponent signals is discussed. The influence of the scaling factors used for the visualization of the signal in a two-dimensional plane is also studied.