Nonlinear analysis of cyclically correlated spectral spreading in modulated signals

Abstract

This paper examines the mapping from the Cohen class of bilinear time-evolutionary spectral estimators (TES) to a conjoint frequency-cycle frequency signal description for modulated acoustic signals. The transform mapping provides a cycle spectrum estimation that is used to identify cyclostationarity in modulated acoustic signals that often remains undetected in the one-dimensional time history and power spectral density (PSD). The Wigner distribution (WD) TES is derived as the case for which the PSD used in stationary analysis of acoustic signals is preserved in the Fourier transform mapping to a conjoint frequency–frequency correlation signal representation for modulated signals. Fourier transformation over temporal window centers of a pseudo-WD TES of modulated acoustic signals is shown to equate to the time-variant cyclic spectrum, defined for cyclostationary signals, evaluated along the center of a moving average estimate. A pseudo-WD TES based function mapping procedure for cycle frequency estimation of modulated acoustic signals is presented and applied to several modulated signal examples. These include the acoustic reflection from a periodically vibrating object, frequency hopped pulse trains, and bi-phase modulated continuous wave sonar signals. The function solution is shown to achieve cycle frequency estimation in −3-dB signal-to-noise.