Fitting ARMA Models to linear non-Gaussian processes using higher order statistics
Signal Processing - Image and Video Coding beyond Standards
Quadratic Estimation of Multivariate Signals from Randomly Delayed Measurements*
Multidimensional Systems and Signal Processing
Adaptive nonlinear system identification in the short-time fourier transform domain
IEEE Transactions on Signal Processing
Approximation theory on manifolds
MACMESE'09 Proceedings of the 11th WSEAS international conference on Mathematical and computational methods in science and engineering
Modeling and identification of nonlinear systems in the short-time fourier transform domain
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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Volterra filters (VFs) and higher order statistics (HOS) are important tools for nonlinear analysis, processing, and modeling. Despite their highly desirable properties, the transfer of VFs and HOS to real-world signal processing problems has been hindered by the requirement of very large data records needed to obtain reliable estimates. The identification of VFs and the estimation of HOS both fall into the category of ill-posed estimation problems. We develop penalized least squares (PLS) estimation methods for VFs and HOS. It is shown that PLS is a very effective way to incorporate prior information of the problem at hand without directly constraining the estimation procedure. Hence, PLS produces much more reliable estimates. The main contributions of this paper are the development of appropriate penalizing functionals and cross-validation procedures for PLS based VF identification and HOS estimation