1 October 1992 Acousto-optic estimation of correlations and spectra using triple correlations and bispectra
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The relationships between lower and higher order cumulants of deterministic and random continuous signals are presented. This theory is used to develop time- and frequency-domain algorithms for the estimation of correlations (spectra) from triple correlations (bispectra) using acousto-optic processors. Cumulants are of interest because they are insensitive to a wide class of additive noises, including Gaussian noise of unknown covariance. Thus, noise-insensitive correlation (spectrum) estimates can be derived from higher order correlations (polyspectra). The potential for noise insensitivity is examined through the variance of power spectrum estimates based on conventional (second-order) and bispectrum statistics. A proof-of-principle experiment was carried out using an acousto-optic four-product processor to estimate the autocorrelation of a wideband periodic signal. The experimental data are compared with a simulation to validate the results.
Brian M. Sadler, Georgios B. Giannakis, Dale J. Smith, "Acousto-optic estimation of correlations and spectra using triple correlations and bispectra," Optical Engineering 31(10), (1 October 1992). https://doi.org/10.1117/12.58873

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