Narrowband acoustic Doppler volume backscattering signal .I. Evolutionary spectral analysis

This paper examines the statistical properties of the narrowband Doppler volume backscattering process and analyzes its evolutionary spectrum. After clarifying the mechanism of both the finite duration Doppler effect and the continuously space-shifted integration process, the first two order time-varying statistics under a more general assumption, i.e., von Mises distribution, of random phase are derived. The generalization permits nonuniform phase tendency, which occurs in layered medium scattering. Based on the locally stationary process model, the evolutionary spectrum of the signal is derived. It is shown that the variation of the backscattering strength enters the spectrum as an amplitude modulation, whereas the variation of the random phase distribution acts as both the amplitude modulation and the frequency modulation. Finally, the observability of the average flow speed using the spectral centroid estimate is discussed.