Nonlinear system compensation based on orthogonal polynomial inverses

A Robust Nonlinear System Identification Algorithm using Orthogonal Polynomial Network

Inverses of Polynomial Functions

Let (K, 3) be a (commutative) topological field. (We do not require that multiplicative inversion be continuous, i.e. 3 is a ring topology. See [l, p. 274] for the definition of the latter.) Throughout this paper, 11 will denote a basic system of neighborhoods of zero for 3. Let P(X) be a polynomial in K[X] of degree »sS2, and let S= {P(a)\a£EK}. We will be concerned with suitably defining a mu...

Fingerprint Recognition using Orthogonal Polynomial Based Transform

Biometric features such as face, iris, voice, retina, handwriting and fingerprint plays an important role in security for authentication. Among biometrics, fingerprint systems have been one of most widely researched and deployed because of their easy access and low price of fingerprint sensors. Nowadays, for personal identification automatic fingerprint recognition is preferred due to their rel...

On orthogonal polynomials obtained via polynomial mappings

Let (pn)n be a given monic orthogonal polynomial sequence (OPS) and k a fixed positive integer number such that k ≥ 2. We discuss conditions under which this OPS originates from a polynomial mapping in the following sense: to find another monic OPS (qn)n and two polynomials πk and θm , with degrees k and m (resp.), with 0 ≤ m ≤ k − 1, such that pnk+m(x) = θm(x)qn(πk(x)) (n = 0, 1, 2, . . .). In...

Orthogonal polynomial expansions on sparse grids

We study the orthogonal polynomial expansion on sparse grids for a function of d variables in a weighted L space. A fast algorithm is developed to compute the orthogonal polynomial expansion by combining the fast cosine transform, a fast transform from the Chebyshev orthogonal polynomial basis to the orthogonal polynomial basis for the weighted L space, and a fast algorithm of computing hierarc...