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TitleThe development of instantaneous bandwidth via local signal expansion
Publication TypeJournal Article
Year of Publication1993
AuthorsPoletti, M.A.
JournalSignal Processing
Pagination273 - 281
Date Published1993
ISSN01651684 (ISSN)
KeywordsInstantaneous bandwidth development, Iterative methods, Local signal expansion, MATHEMATICAL MODELS, Phase control, Phase measurement, Signal processing, Spectrum Analysis, Taylor series expansion, Wigner Ville distribution
AbstractRecently 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. © 1993.

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