| Title | The development of instantaneous bandwidth via local signal expansion |
| Publication Type | Journal Article |
| Year of Publication | 1993 |
| Authors | Poletti, M.A. |
| Journal | Signal Processing |
| Volume | 31 |
| Issue | 3 |
| Pagination | 273 - 281 |
| Date Published | 1993 |
| ISSN | 01651684 (ISSN) |
| Keywords | Instantaneous bandwidth development, Iterative methods, Local signal expansion, MATHEMATICAL MODELS, Phase control, Phase measurement, Signal processing, Spectrum Analysis, Taylor series expansion, Wigner Ville distribution |
| Abstract | 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. © 1993. |
| URL | http://www.scopus.com/inward/record.url?eid=2-s2.0-0027575521&partnerID=40&md5=ad486910806396c0da469a9e10ad0795 |
| DOI | 10.1016/0165-1684(93)90086-P |
