By using complex variable methods (steepest descent and residues) to asymptotically evaluate the coefftcient integrals, the numerical analysis of Hermite function series is discussed. There are striking similarities and differences with the author’s earlier work on Chebyshev polynomial methods (J. Comp. Phys. 45 (1982), 45-49) for infinite or semi-infinite domains. Like Chebyshev series, the He...

A coherent mathematical framework for the psychophysics of contrast perception emerges when contrast sensitivity is posed as an eigenvalue problem. This more general mathematical theory is broad enough to encompass Fourier analysis as it is used in vision research. We present a model of space-variant contrast detection to illustrate the main features of the theory, and obtain a new contrast sen...

The Hermite Normal Form is a canonical matrix analogue of Reduced Echelon Form, but involving matrices over more general rings. In this work we formalise an algorithm to compute the Hermite Normal Form of a matrix by means of elementary row operations, taking advantage of the Echelon Form AFP entry. We have proven the correctness of such an algorithm and refined it to immutable arrays. Furtherm...

In this work, we investigate the parallel-beam projection and reconstruction of band-limited Hermite expansions. Using a recently developed coordinate conversion technique, we show how the Fourier slice theorem can be directly applied. In our new approach, we do not introduce a non-integrable filter that appears in the filtered backprojection method. Since a projection of a 2D band-limited Herm...

We investigate the asymptotic behavior for type II Hermite-Padé approximation to two functions, where each function has two branch points and the pairs of branch points are separated. We give a classification of the cases such that the limiting counting measures for the poles of the Hermite-Padé approximants are described by an algebraic function h of order 3 and genus 0. This situation gives r...

A procedure for combined image watermarking and compression, based on the Hermite projection method is proposed. The Hermite coefficients obtained by using the Hermite expansion are used for watermark embedding. The image can be efficiently reconstructed by using a set of Hermite coefficients that is quite smaller than the number of original ones. Hence, the watermark embedding is actually done...

Hermite subdivision schemes have been studied by Merrien, Dyn and Levin and they appear to be very different from subdivision schemes analyzed before since the rules depend on the subdivision level. As suggested by Dyn and Levin, it is possible to transform the initial scheme into a uniform stationary vector subdivision scheme which can be handled more easily. With this transformation, the stud...

Vector and Hermite subdivision schemes both act on vector data, but since the latter one interprets the vectors as function values and consecutive derivatives they differ by the “renormalization” of the Hermite scheme in any step. In this paper we give an algebraic factorization method in one and several variables to relate any Hermite subdivision scheme that satisfies the so–called spectral co...

In this manuscript, we introduce concepts of (m1,m2)-logarithmically convex (AG-convex) functions and establish some Hermite-Hadamard type inequalities of these classes of functions.

In this paper, we consider the design of pulse shaping filter using orthogonal Hermite-Rodriguez basis functions. The pulse shaping filter design problem has been formulated and solved as a quadratic programming problem with linear inequality constraints. Compared with the existing approaches reported in the literature, the use of Hermite-Rodriguez functions offers an effective alternative to s...