Detection of Oscillatory and Impulsive Transients Using Higher Order Correlations and Spectra

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Physics and Astronomy


Mathematics and Natural Sciences


Higher-order cross and ordinary correlation detectors are applied to four deterministic transients contaminated by uncorrelated Gaussian noise only. Histograms and moments are used to examine the properties of the signals and their effect on detector performance. Receiver operating characteristic (ROC) curve analysis and limiting signal-to-noise ratios for "good" detection provide comparative measures for different detectors. Probability density functions of detection ordinate values of signal-present and noise-only correlations are used to explain ROC curve behavior. Using a known source, the cross-correlation detector performs better than the higher-order correlation detectors for each transient studied. However, for an unknown narrow pulse source signal, the bicorrelation and tricorrelation detectors outperform the cross-correlation detector. In contrast, the bicorrelation detector performs very poorly for low-frequency narrow-band signals with a small third moment embedded in uncorrelated Gaussian noise. Rectification as part of the detection process improves the performance of the bicorrelation detector and also places the peak of maximum magnitude at the origin. This eliminates the problem in detection or time delay estimation that the existence of multiple peaks due to symmetries in the auto-bicorrelation or the bicorrelation of repeated signals may cause. The tricorrelation detector also performs better with rectification than without. For an unknown source, the bicorrelation and tricorrelation detectors with rectification perform on a level comparable to the cross-correlation detector for certain signals. Comparisons are made between repeating a known source and repeating noisy received signals in the bicorrelation.

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Journal of the Acoustical Society of America





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