The Wiener-Khintchine theorem dictates that the correlation function of any stationary, stochastic signal y(t) has as its Fourier transform a function that is necessarily both real and non-negative. In this paper, I explore the real-space, geometric consequences of this reciprocal-space non-negativity constraint. I review prior results addressing this issue, and I also introduce a family of new...

Design of controller for the process operation is typically based on the availability of the best model. Development of empirical model is incorporated with many assumptions and approximations. System identification is developed to alleviate this problem by considering the input and output data of the process for the model development. The cascaded tank process is highly nonlinear and non-minim...

Image and video signals are sometimes corrupted by Gaussian noise. Wiener ltering could reduce noise eeectively. Wiener lter is the best linear restoration lter in the sense of mean square error (MSE). In this project, Wiener lters were implemented to reduce noise in noisy images and video sequences. The lter taps of Wiener lter adapt with local signal and noise statistics. This report has four...

We present a novel method for Wiener system identification. The method relies on a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process model for the static nonlinearity. We avoid making strong assumptions, such as monotonicity, on the nonlinear mapping. Stochastic disturb...

Let us consider the process (X (α) t )t∈[0,T ) given by the SDE dX (α) t = − α T−t X (α) t dt+ dBt, t ∈ [0, T ), where α ∈ R, T ∈ (0,∞), and (Bt)t>0 is a standard Wiener process. In case of α > 0 the process X(α) is known as an α-Wiener bridge, in case of α = 1 as the usual Wiener bridge. We prove that for all α, β ∈ R, α 6= β, the probability measures induced by the processes X(α) and X(β) are...