18 September 1998 Local spectral and temporal characterizations of a wave
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Many waves exhibit characteristics that depend on time and/or frequency. For example, the frequencies of a pulse propagating in a dispersive medium travel at different velocities. This kind of dependency gives rise to the need for joint time- frequency analysis and methods for describing the local temporal and spectral nature of waves, particularly pulses and transients. Useful concepts arising for this description from time-frequency theory are the average frequency at each time of a wave, and the spread about that average. These quantities are obtained as conditional moments of a time-frequency density (TFD). We explore the conditional variances of some common TFDs, and determine when these are positive (which isn't always the case). We also investigate local characteristics of a wave, in terms of these conditional moments, and show through experimental results that they robustly characterize the time-frequency behavior of transients and pulses.
© (1998) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Patrick J. Loughlin, Patrick J. Loughlin, } "Local spectral and temporal characterizations of a wave", Proc. SPIE 3371, Automatic Target Recognition VIII, (18 September 1998); doi: 10.1117/12.323873; https://doi.org/10.1117/12.323873

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