An optimal nonlinear filter for detecting non-normality in a signal using the bicoherence

Jonathan M. Nichols; Colin Olson; Joseph Michalowicz; Frank Bucholtz

doi:10.1117/12.818483

11 May 2009 An optimal nonlinear filter for detecting non-normality in a signal using the bicoherence

Jonathan M. Nichols, Colin Olson, Joseph Michalowicz, Frank Bucholtz

Proceedings Volume 7336, Signal Processing, Sensor Fusion, and Target Recognition XVIII; 73361D (2009) https://doi.org/10.1117/12.818483
Event: SPIE Defense, Security, and Sensing, 2009, Orlando, Florida, United States

Abstract

Higher-order spectral analysis is one approach to detecting deviations from normality in a received signal. In particular the auto-bispectral density function or "bispectrum" has been used in a number of detection applications. Both Type-I and Type-II errors associated with bispectral detection schemes are well understood if the processing is performed on the received signal directly or if the signal is pre-processed by a linear, time invariant filter. However, there does not currently exist an analytical expression for the bispectrum of a non-Gaussian signal pre-processed by a nonlinear filter. In this work we derive such an expression and compare the performance of bispectral-based detection schemes using both linear and nonlinear receivers. Comparisons are presented in terms of both Type-I and Type-II detection errors using Receiver Operating Characteristic curves. It is shown that using a nonlinear receiver can offer some advantages over a linear receiver. Additionally, the nonlinear receiver is optimized using genetic programming (differential evolution) to choose the filter coefficients.

Citation Download Citation

Jonathan M. Nichols, Colin Olson, Joseph Michalowicz, and Frank Bucholtz "An optimal nonlinear filter for detecting non-normality in a signal using the bicoherence", Proc. SPIE 7336, Signal Processing, Sensor Fusion, and Target Recognition XVIII, 73361D (11 May 2009); https://doi.org/10.1117/12.818483

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