Abstract. Recently efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized sinc functions. This article studies the error of the reconstructed non-bandlimited signal when an adaptive truncation scheme is employed. Further, wh...

The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral representations of the Green’s functions by Sinc function expansions are an extremely powerful calculative tool. Specifically, this understanding makes it not on...

The sinc-collocation method is presented for solving a nonlinear system of second-order boundary value problems. Some properties of the sinc-collocation method required for our subsequent development are given and are utilized to reduce the computation of solution of the system of second-order boundary value problems to some algebraic equations. Numerical examples are included to demonstrate th...

Linguistic labels affect inductive generalization; however, the mechanism underlying these effects remains unclear. According to one similarity-based model (SINC: Similarity-Induction-NamingCategorization), early in development labels are features of objects contributing to the overall similarity of compared entities, with early induction being similarity-based. If this is the case, then not on...

In this paper we solve two biharmonic problems over a square, B = (−1, 1) × (−1, 1). (1) The problem ∇4U = f , for which we determine a particular solution, U , given f , via use of Sinc convolution; and (2) The boundary value problem ∇4V = 0 for which we determine V given V = g and normal derivative Vn = h on ∂B, the boundary of B. The solution to this problem is carried out based on the identity

We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The are given in terms convolution, our proposed numerical approach is not only super-algebraically convergent, but it also satisfies an important property convolution—namely, preservation bandwidth. Furthermore, accuracy depends how well source field approx...

Introduction: Hadamard-encoded (H-encoded) fMRI [1] is a method that acquires a slab of multiple subslices with each RF excitation [2]. The subslices can then be extracted using temporal filtering, analogous to UNFOLD [3]. By setting the subslice width equal to that of a conventional fMRI scan, SNR is increased because of the larger slab thickness. However, since H-encoding uses complex data fo...