Volterra filtering and higher order whiteness

Some properties of Volterra filtering are established. Finite-order, finite-horizon Volterra filtering is investigated as well as its asymptotic properties. Next, the concepts of Volterra unpredictability and uninterpolability lead to generalizations of the notion of white noise to higher orders. These generalizations are introduced and relations are established between them. >

[1]  Wei Lin,et al.  Stabilization of discrete-time nonlinear systems by smooth state feedback , 1993 .

[2]  Anatoly M. Vershik,et al.  Some Characteristic Properties of Gaussian Stochastic Processes , 1964 .

[3]  M. Rosenblatt Stationary sequences and random fields , 1985 .

[4]  Patrick Duvaut,et al.  Optimal linear-quadratic systems for detection and estimation , 1988, IEEE Trans. Inf. Theory.

[5]  Ian F. Blake,et al.  On a class of processes arising in linear estimation theory , 1968, IEEE Trans. Inf. Theory.

[6]  Laurent Schwartz,et al.  Analyse : Topologie générale et analyse fonctionnelle , 1993 .

[7]  Messaoud Benidir,et al.  Polyspectrum modeling using linear or quadratic filters , 1993, IEEE Trans. Signal Process..

[8]  Chong-Yung Chi,et al.  Linear prediction, maximum flatness, maximum entropy, and AR polyspectral estimation , 1993, IEEE Trans. Signal Process..

[9]  J. William Helton,et al.  NonlinearH∞ control theory for stable plants , 1992, Math. Control. Signals Syst..

[10]  Gary L. Wise,et al.  On the design of nonlinear discrete-time predictors , 1982, IEEE Trans. Inf. Theory.

[11]  Albert N. Shiryaev,et al.  On a Method of Calculation of Semi-Invariants , 1959 .

[12]  M. Fréchet Sur les fonctionnelles continues , 1910 .

[13]  R. de Figueiredo The Volterra and Wiener theories of nonlinear systems , 1982, Proceedings of the IEEE.

[14]  Monson H. Hayes,et al.  Estimating 2-D DOA angles using nonlinear array configurations , 1995, IEEE Trans. Signal Process..

[15]  Vinod Chandran,et al.  A general procedure for the derivation of principal domains of higher-order spectra , 1994, IEEE Trans. Signal Process..