Algorithmic Selection of Acoustic Waveforms

The choice of acoustic waveform is studied within the category of widely spaced FM pulses for the goal of optimum resolution between overlapping arrivals. For a given average frequency and pulse time length, it is analytically apparent that there exists a wide variety of monotonic F-t shapes that have the same average frequency, time length or number of cycles, and frequency difference between initial and final cycles. It is then shown how to program the calculation of autocovariance among all such waveforms using a preliminary calculation of a subset of the partitions of an integer sum representing the pulse time length. The number of integers in the partition is restricted to be the number of cycles with the smallest integer representing the highest frequency and the largest representing the lowest. The most prevalent choice, for an optimum decline among the autocovariance side-lobe peaks, has a frequency variation that is small at the ends of the pulse and high near the center. It is also possible to seek along the courses of spreading the frequency extremes and changing the pulse length for F-t shapes that further minimize the side lobes. [Hudson Labs. of Columbia Univ. Informal Documentation No. 137. This work was supported by the U. S. Office of Naval Research.]