Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
An investigation of the second- and higher-order spectra of music
Signal Processing
Multitaper estimators of polyspectra
Signal Processing
Asymptotic Bias and Variance of Conventional Bispectrum Estimates for 2-D Signals
Multidimensional Systems and Signal Processing
The Volterra and Wiener Theories of Nonlinear Systems
The Volterra and Wiener Theories of Nonlinear Systems
A comparison of optimized higher order spectral detectiontechniques for non-Gaussian signals
IEEE Transactions on Signal Processing
A time-domain test for some types of nonlinearity
IEEE Transactions on Signal Processing
Coloring Non-Gaussian Sequences
IEEE Transactions on Signal Processing
The degradation of higher order spectral detection using narrowbandprocessing
IEEE Transactions on Signal Processing
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In the analysis of data from nonlinear systems both the bispectrum and the bicoherence have emerged as useful tools. Both are frequently used to detect the influence of a nonlinear system on the joint probability distribution of the system input. Previous work has provided an analytical expression for the bispectrum of a quadratically nonlinear system output if the input is stationary, jointly Gaussian distributed. This work significantly generalizes the previous analysis by providing an analytical expression for the bispectrum of the response of quadratically nonlinear systems subject to stationary, jointly non-Gaussian inputs possessing arbitrary auto-correlation function. The expression is then used to determine the optimal input probability density function for detecting a quadratic nonlinearity in a second-order system. It is also shown how the expression can be used to design an optimal nonlinear filter for detecting deviations from normality in the probability density of a signal.