Analysis of Time-Varying Spatially-Varying Sound-Propagation Systems
It has proven very useful in the analysis of signal processing for sonar systems to represent signals by cross-ambiguity functions and system — such as a target or the medium — that modify the signal by spreading or scattering functions. These functions measure respectively how signals are spread and how systems spread signals in time and frequency. In such systems, sound-propagation paths play a significant part. This paper presents an extension of the temporal theory to consider spatial variations: as before, signals are represented by cross-ambiguity functions and systems by spreading or scattering functions; however, in the extension, spreads in space and wave number are considered in addition. A major cause of such spreads is often bottom interactions. Two versions of the spatial theory are presented: a free-space version for use when ray theory is applicable and a layered-media version for use when it is not. In the layered-media version a normal-mode model of propagation is assumed and spreads occur in mode number as well as wave number. If the transmitted signal is assumed to be a plane wave modulated by a narrow-band time signal, the ambiguity function for the transmitted signal is the product of the temporal ambiguity function of the time signal and the beam pattern for the receiving array.
KeywordsCovariance Radar Coherence Convolution Acoustics
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