The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-190

“Bispectra for Sonar”

by Jerry M. Mendel

October 1991

The usefulness of polyspectra, and mixed moments of both integer and rational orders, in detecting and quantifying various kinds of frequency and phase couplings is studied. Both the deterministic and random cases are considered. Several interesting issues regarding frequency coupling in deterministic signals, and detection of phase coupling in the absence of frequency coupling are addressed. In particular, the problem of estimating rational phase-coupling in sonar signal processing is considered. One approach first estimates the frequencies, amplitudes and phases, and then performs a rational phase-coupling hypothesis test on whether the estimated phases bear the same ratios as their corresponding frequencies. Although high-resolution estimates of the frequencies can be obtained using the fourth-order cumulants, the estimated phase have to be "unwrapped" owing to the modulo-2π problem. It is not clear how this can be done. Hence, this approach for unraveling rational phase-coupling seems to be infeasible. Another approach using higher-order mixed moment functions and fractional moments is introduced and studied. It is shown that this approach can detect unconventional types of frequency and phase coupling.

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