Testing for nonlinearity in time series: the method of surrogate data
Conference proceedings on Interpretation of time series from nonlinear mechanical systems
Nonlinear model-based control using second-order Volterra models
Automatica (Journal of IFAC)
Physica D
Cross-Bispectrum Computation and Variance Estimation
ACM Transactions on Mathematical Software (TOMS)
Time series: data analysis and theory
Time series: data analysis and theory
Blind equalizers of multichannel linear-quadratic FIR Volterra channels
SSAP '96 Proceedings of the 8th IEEE Signal Processing Workshop on Statistical Signal and Array Processing (SSAP '96)
Identification of structurally constrained second-order Volterramodels
IEEE Transactions on Signal Processing
IEEE Transactions on Neural Networks
A robust subpixel motion estimation algorithm using HOS in the parametric domain
Journal on Image and Video Processing - Special issue on patches in vision
Improved bispectrum based tests for Gaussianity and linearity
Signal Processing
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In this paper we discuss the efficiency of nonlinearity indices based on higher order statistics in order to detect nonlinearities in an observed signal, the signal being the output of a transmission channel (possibly nonlinear) tile input of which is not accessible. Nonlinearity detection is the first step of nonlinearity analysis, this step being followed by nonlinearity location of the nonlinear components (in the Fourier domain) and quantification of these components. The main results reported in this paper are, first, a systematic survey of the robustness of hypothesis testing for each index and, second, the derivation of indices which neither involve the ratio of estimated quantities (such as bicoherence) nor phase unwrapping (such as the bicepstrum). The robustness of hypothesis testing is verified by calculating type II error probability (i.e. the error of declaring that the time series has been produced by a linear system while produced by a nonlinear one). To calculate this error, the observed time series is assumed to be the output of a second-order Volterra model driven by a Gaussian distributed noise. Obviously, the assumption of such a model might seem restrictive, but the results obtained allow us to draw some definitive conclusions about the robustness of the indices presented. The calculation is performed first from a theoretical spectrum and bispectrum and, second, from estimated indices. These indices are estimated from linear and nonlinear time series having the same spectrum. The estimation of the type II error probability on estimated indices allows the verification of the assumptions used to derive the theoretical index probability density function.