Alternative signal processing models for broadband underwater propeller sounds.

Abstract

Underwater propeller sounds often have audibly rhythmic characteristics. These sounds are commonly modeled as a broadband noise carrier multiplied by a rhythmic modulator, where analysis of the modulator wave form can provide information relating to the speed and identity of the source vessel. A natural assumption is to posit a purely periodic modulator, considering the rotary action of the propeller, which is useful for deriving maximum-likelihood estimates of the shaft rate [Lourens and du Preez, J. Ocean. Eng. 23, 4, (1998)]. Indeed, recorded propeller data are unmistakably rhythmic, but the assumption of a strictly periodic or cyclical modulator wave form is questionable. A critical analysis of the periodicity assumption is presented and compared to three alternatives. Maintaining the product form in which the modulator wave form multiplies a random broadband carrier, the possible modulator signals are generalized to include: (1) almost-periodic functions expressible by nonharmonic trigonometric series; (2) multiplicative cascades of possibly complex-valued modulator functions; and (3) stochastic processes in which random state transitions constitute a sense of repeatability or rhythm. In this work, three modulator models are contrasted as estimators of periodicity, using actual propeller sound recordings to validate these estimates. [This work is supported by the Office of Naval Research.]