Lattice theory models for space-time sampling of acoustic signals

Abstract

The space-time sampling of underwater acoustic signals by both fixed and towed arrays of sensors can be modeled by lattice theory. The sampling schedule of a fixed array produces a rectangular space-time lattice while the sampling schedule of an array towed at a uniform velocity produces a trapezoidal lattice. Changing the velocity of a towed array corresponds to changing the skewness of a trapezoidal lattice. Willis and Bresler [IEEE Info. Theory (1997)] established an upper bound on the space-time-bandwidth product of a signal that can be sampled time sequentially by a lattice without aliasing. This upper bound provides a valuable perspective on the tradeoff among the temporal intersample interval, the interelement spacing of sensors, the velocity of the towed array, and the spectral support of signal that can be sampled without aliasing. A towed array with the same interelement spacing and temporal intersample interval can sample signals with broader spectral support than a fixed array. Alternately, a towed array can sample a signal with the same spectral support at a slower rate than an equivalent fixed array decreasing load on the data processing system. [Work supported by ONR.]