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

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