Abstract Bio-signals are extensively used in diagnosing many diseases wearable devices. In signal processing, reconstruction is one of the essential applications. Discrete orthogonal moments (DOMs) effective analysis tools for signals that can extract digital information without redundancy. The propagation numerical errors a significant challenge computation DOMs at high orders. This problem da...

Recently it was found [1] that polynomial solutions of differential equations are connected to finite-dimensional representations of the algebra sl2 of firstorder differential operators. In this Talk it will be shown that there also exists a connection between polynomial solutions of finite-difference equations (like Hahn, Charlier and Meixner polynomials) and unusual finitedimensional represen...

W. Mittlefehldt, D. K. Ross, R. C. Greenwood, M. Anand, I. A. Franchi, M. M. Grady, and B. L. A. Charlier. Department of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK (Email: [email protected]), Astromaterials Research Office, NASA Johnson Space Center, Houston, TX, 77058, USA, Jacobs Technology, 2224 Bay Area Blvd. Houston Tx 77058, USA, Department of ...

Given a stochastic process X = {Xt, t ∈ R+} with finite moments of convenient order, a time–space harmonic polynomial relative to X is a polynomial Q(x, t) such that the process Mt =Q(Xt, t) is a martingale with respect to the filtration associated with X . Major examples are the Hermite polynomials relative to a Brownian motion, the Charlier polynomials relative to a Poisson process and the La...

In this paper, we address the problem of separation of mutually independent sources in nonlinear mixtures. First, we propose theoretical results and prove that in the general case, it is not possible to separate the sources without nonlinear distortion. Therefore, we focus our work on specific nonlinear mixtures known as post-nonlinear mixtures. These mixtures constituted by a linear instantane...

There are two major approaches for blind separation: Maximum Entropy (ME) and Minimum Mutual Information (MMI). Both can be implemented by the stochastic gradient descent method for obtaining the de-mixing matrix. The MI is the contrast function for blind separation while the entropy is not. To justify the ME, the relation between ME and MMI is rstly elucidated by calculating the rst derivative...