THE DEVELOPMENT OF INSTANTANEOUS BANDWIDTH VIA LOCAL SIGNAL EXPANSION

Recently the squared instantaneous bandwidth of a signal has been defined as the conditional spectral variance of a time-frequency distribution of the signal at a given time. However, the value of the instantaneous bandwidth depends on the choice of the distribution. Cohen and Lee have derived a class of distributions for which the conditional spectral variance is always positive, and argue that it is therefore a plausible candidate for the definition of instantaneous bandwidth. A new method is presented here for defining the instantaneous bandwidth, based on the local modelling of a signal as a constant frequency with a varying envelope. The model is obtained from a Taylor series expansion of the log magnitude and phase. Since the method is based only on properties of the signal, it does not require the use of time-frequency distributions. A first-order magnitude signal expansion produces an instantaneous half-power bandwidth equal to the instantaneous bandwidth proposed by Cohen and Lee. A second-order magnitude expansion produces an instantaneous bandwidth equal to that of the Wigner-Ville distribution. An alternative definition of instantaneous bandwidth based on a second-order expansion of the phase is also examined. This definition produces an instantaneous bandwidth squared proportional to the phase curvature, and is consistent with time-frequency distributions with particular kernel properties. A comparison is made between the three forms of instantaneous bandwidth. It is shown that the phase- and magnitude-based definitions are similar for minimum phase signals.