Acousto-optic estimation of autocorrelation and spectra using triple correlations and bispectra

Nonparametric estimation of lower-order statistics from higher-order statistics of continuous processes is considered. Of particular interest is estimation of correlations and spectra (second-order statistics) from higher-order correlations and polyspectra (higher-order statistics). The use of higher-order statistics is motivated by their insensitivity to a wide class of additive noises including Gaussian noise of unknown covariance. The fact that lower-order correlations are projections of higher-order correlations is exploited. Experimental results are presented using an acousto-optic triple product processor to estimate the autocorrelation of a 1- D signal.