Given a convex rational polytope b = x ∈ n+ Ax= b , we consider the function b → f b , which counts the nonnegative integral points of b . A closed form expression of its -transform z → z is easily obtained so that f b can be computed as the inverse -transform of . We then provide two variants of an inversion algorithm. As a by-product, one of the algorithms provides the Ehrhart polynomial of a...

A system (Pα : α ∈ A) of probability measures on a common state space S indexed by another index set A can be “realized” by a system (Xα : α ∈ A) of S-valued random variables on some probability space in such a way that each Xα is distributed as Pα. Assuming that A and S are both partially ordered, we may ask when the system (Pα : α ∈ A) can be realized by a system (Xα : α ∈ A) with the monoton...

We propose a matrix approach to the computation of Battle-Lemari e's wavelets. Since the Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a b-spline of order m. The polynomial is the symbol of an bi-innnite matrix B associated with b-spline of order 2m. We approximate B 2m by its nit...

The Fourier transforms x̂j = ∑ k xkω , k, j = 0, 1, . . . , n− 1 of a data vector x with scalar components xk indexed by n-fold planar rotations ω k define a n × n Hermitian matrix F with entries ωjk/√n, so that x̂ = √n Fx and the inverse Fourier transform is simply x = F∗x̂/√n. Here, the frequencies ω and their harmonics ω fully describe the set (Ĝ) of all n irreducible representations of the Abe...

An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method. (Dubner and Abate, 1968). The advantages of this modified procedure are twofold: first, the error bound on the inverse f{t) becomes independent of t, instead of being exponential in t; second, and consequently, the trigonometric series obtained for fit)...

The 9/7 wavelet is used for a wide variety of image compression tasks. Recent research, however, has established a methodology for using evolutionary computation to evolve wavelet and scaling numbers describing transforms that outperform the 9/7 under lossy conditions, such as those brought about by quantization or thresholding. This paper describes an investigation into which of three possible...

This paper is about a new efficient method for the implementation of convolvers and correlators using the Fermat Number Transform (FNT) and the inverse (IFNT). The latter present advantages compared to Inverse Fast Fourier Transform (IFFT). An efficient state space method for implementing the Inverse FNT (IFNT) over rectangular windows is proposed for the cases where there is a large overlap be...

INTRODUCTION A novel image reconstruction technique, which avoids aliasing artifacts by scalable image reconstruction in Magnetic Resonance Imaging, is proposed. The signal obtained in the phase-scrambling Fourier imaging technique can be transformed to the signal described in the Fresnel transform equation of the objects. Therefore, image reconstruction can be performed not only by inverse Fou...