This paper presents a novel Wiener-type recurrent neural network with the observer/Kalman filter identification (OKID) algorithm for unknown dynamic nonlinear system identification. The proposed Wiener-type recurrent network resembles the conventional Wiener model that consists of a dynamic linear subsystem cascaded with a static nonlinear subsystem. The novelties of our approach include: (1) t...

—We address the problem of linear minimum meansquared error (LMMSE) estimation under constraints on the lter or the estimated signal. We develop a general formula that leads to closed form solutions for a wide class of constrained LMMSE problems. The results are applicable to both nite dimensional problems as well as to the Wiener ltering setup, in which in nitely-many measurements are availabl...

In this thesis, we study the theory of Isotropic Multiresolution Analysis (IMRA) and its application to image analysis problems that require rotational invariance. Multiresolution Analysis (MRA) is a mathematical tool that gives us the ability to process a signal or an image at multiple levels of resolution and detail. IMRA is a new type of MRA for which the core resolution sub-space is invaria...

In this paper we present a simple closed-form solution to the Wiener–Hammerstein (W–H) identification problem. The identification process occurs in the log-frequency domain where magnitudes and phases are separable. We show that the theoretically optimal W–H identification is unique up to an amplitude, phase and delay ambiguity, and that the nonlinearity enables the separate identification of t...

We generalize the theory of Wiener amalgam spaces on locally compact groups to quasi-Banach spaces. As a main result we provide convolution relations for such spaces. Also we weaken the technical assumption that the global component is invariant under right translations, which is even new for the classical Banach space case. To illustrate our theory we discuss in detail an example on the ax + b...

The function u(t) need not be a member of C, but can be any Borel measurable function defined on OSj/^1, and may even be permitted to take on infinite values. The Wiener integral of a functional is simply the Lebesgue integral of the functional with respect to Wiener's measure [4]1 in C. This measure is not invariant under translations, but is in other respects a Lebesgue measure based on inter...

We give a new proof of the well-known fact that the pinned Wiener measure on a Lie group is quasi-invariant under right multiplication by 1nite energy paths. The main technique we use is the time reversal. This approach is di3erent from what B. Driver used to prove quasi-invariance for the pinned Brownian motion on a compact Riemannian manifold. c © 2002 Elsevier Science B.V. All rights reserved.

In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost surely for data in a Fourier-Lebesgue space FL(T) with s ≥ 1 2 , 2 < r < 4, (s − 1)r < −1 and scaling like H 1 2 (T), for small ǫ > 0. We also show the invari...

We prove absolute continuity of Gaussian measures associated to complex Brownian bridges under certain gauge transformations. As an application we prove that the invariant measure for the periodic derivative nonlinear Schrödinger equation obtained by Nahmod, Oh, Rey-Bellet and Staffilani in [20], and with respect to which they proved almost surely global well-posedness, coincides with the weigh...

Let G= V E be a simple connected graph. The distance between two vertices of G is defined to be the length of the shortest path between the two vertices. There are topological indices assigned to G and based on the distance function which are invariant under the action of the automorphism group of G. Some important indices assigned to G are the Wiener, Szeged, and PI index which we will find th...