A new class of biorthogonal wavelets—interpolating distributed approximating functional (DAF) wavelets are proposed as a powerful basis for scale-space functional analysis and approximation. The important advantage is that these wavelets can be designed with infinite smoothness in both time and frequency spaces, and have as well symmetric interpolating characteristics. Boundary adaptive wavelet...

V. M. Sloutsky and A. V. Fisher reported 5 experiments documenting relations among categorization, induction, recognition, and similarity in children as well as adults and proposed a new model of induction, SINC (similarity, induction, categorization). Those authors concluded that induction depends on perceptual similarity rather than conceptual knowledge. Despite the useful contributions of th...

This work proposes k-space filters with the option to fine-tune filter's strength. The application is in MRI imaging. novelty of this paper multiplication filtering functions by Sinc Function so as obtain Sinc-shaped convolving function. effect visible where a central region formed and it acts filter. Worth noting Figure 12 finesse high-frequency components depicted intensity-curvature function...

We prove that the Toeplitz binary value matrix inversion associated with mth order E-spline interpolation can be implemented using only 2 (m + 1) additions. We develop pipelined architectures for real time B-spline interpolation based on simple running average filters. We also show that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can b...

A quick and accurate way to rotate and shift nuclear magnetic resonance (NMR) images using the two-dimensional chirp-z transform is presented. When the desired image grid is rotated and shifted from the original grid due to patient motion, the chirp-z transform can reconstruct NMR images directly onto the ultimate grid instead of reconstructing onto the original grid and then applying interpola...

In this paper, we prove a conjecture, which was proposed by Frank Stenger in 1997, concerning the localization of eigenvalues of the Sinc matrix I(−1), a problem that is important in both the theory and the practice of Sinc methods. In 2003, Iyad Abu-Jeib and Thomas Shores established a partial answer to this unsolved problem. The techniques they have developed, however, turn out to be the key ...

We resolve and further study a sinc integral evaluation, first posed in this Monthly in [1967, p. 1015], which was solved in [1968, p. 914] and withdrawn in [1970, p. 657]. After a short introduction to the problem and its history, we give a general evaluation which we make entirely explicit in the case of the product of three sinc functions. Finally, we exhibit some more general structure of t...

Transmission from four cases of bovine spongiform encephalopathy (BSE) to mice resulted in neurological disease in 100% of recipient animals, after incubation periods of between 265 and 700 days post-injection. The results from the four cases were very similar to one another. There were major differences in the incubation period between the four inbred strains of mice tested, and even between s...

We address a problem of sampling and reconstructing periodic piecewise polynomials based on the theory for signals with a finite rate of innovation (FRI signals) from samples acquired by a sinc kernel. This problem was discussed in a previous paper. There was, however, an error in a condition about the sinc kernel. Further, even though the signal is represented by parameters, these explicit val...

Green’s functions represent the scattering behaviour of a particular geometry and are required to propagate acoustic disturbances through complex geometries using integral methods. The versatility of existing integral methods of acoustic propagation may be greatly increased by using numerical Green’s functions computed for more general geometries. We investigate the use of the Sinc-Galerkin met...