Compressive Sensing of Cyclic Bispectrum

A method based on higher order cyclostationary statistics is introduced to acquire propeller cavitation noise characteristics. The third-order cyclic cumulant spectrum, also known as the cyclic bispectrum, is derived, and its sparsity is demonstrated for an amplitude-modulated propeller noise model. Cyclic modulation bispectrum (CMBS) is proposed for the feasible approximation of the cyclic bispectrum (CB) based solely on the discrete Fourier transform. A partial Fourier basis is suggested for compressive sensing (CS) of the cyclic modulation bispectrum. The sparse recovery of this bispectrum is formulated as a multiple measurement vector problem. The proposed scheme is suitable, not only for the propeller cavitation noise, but also for general non-Gaussian cyclostationary signals. Numerical examples are given for the acquisition of propeller tonals using real-world underwater acoustic data and synthetically generated propeller noise. Sparse recovery results are compared to the second-order method for various numbers of compressive samples. It is shown that frequencies of the prominent tonals can be obtained even when sampling significantly below the Nyquist rate. The accurate estimation of the tonal magnitudes, on the other hand, is challenging even for a relatively higher number of compressive samples.