To understand the various effects that influence actual flip angles, and correct for these effects, it is important to precisely quantify the MRI parameters (such as T1, T2, and perfusion). In this paper actual flip angle maps are calculated using a conventional gradient-echo (GRE) sequence with different radiofrequency (RF) pulse shapes (Gaussian, sinc, and truncated-sinc), slice-selection gra...

A model of the signal path in arterial spin labeling (ASL)-based functional magnetic resonance imaging (fMRI) is presented. Three subtraction-based methods for forming a perfusion estimate are considered and shown to be specific cases of a generalized estimate consisting of a modulator followed by a low pass filter. The performance of the methods is evaluated using the signal model. Contaminati...

Abstract A previous study by one of the present authors, together with D. Borwein and I. Leonard [8], studied the asymptotic behavior of the p-norm of the sinc function: sinc(x) = (sin x)/x and along the way looked at closed forms for integer values of p. In this study we address these integrals with the tools of experimental mathematics, namely by computing their numerical values to high preci...

We consider approximation of the optimal Yen algorithm for interpolation from a nonuniformly-spaced grid. Although the Yen interpolator is optimal in many senses, it suffers from severe numerical ill conditioning. We suggest a tradeoff between accuracy in computing the interpolator and accuracy in performing the interpolation. A new interpolator is proposed using Choi’s expression for interpola...

The apodization function plays an important role in the behavior of the mean dispersion, group delay and significant reduction of sidelobe level in reflection spectrum. On the other hand, the grating length represents as one of the critical parameters in contributing to a high performance fiber Bragg grating compensator. In this paper, we have investigated and compared the performances of vario...

In orthogonal frequency division multiplexing (OFDM) systems, the subcarriers are generated by an inverse discrete Fourier transform (DFT). OFDM has a relatively slow spectral rolloff. In the literature, the spectra of these subcarriers are often represented by a sequence of sinc functions with the same polarity. This does not explain the intercarrier interference (ICI) cancellation properties ...

In order to make airplane main procedures more efficient and thus s and costs, the distribution of airplane em software will increasingly be p electronically over networks. Sinc software often implements vital func while on the other hand comm networks are in

From previously established results in [2] we develop a simple proof of Keith Ball’s expression in [1] for the volume of the intersection of an (n− 1)dimensional hyperplane with an n-dimensional cube, as well as a simple proof of the formula given by Frank and Riede in [5] for that volume. In our study in [2] of sinc integrals over a decade ago we established results—some of which were recapitu...

The polynomial of degree n which is the best approximation of the sinc function on the interval 0, π/2 with the square norm is considered. By using Lagrange's method of multipliers, we construct the polynomial explicitly. This method is also generalized to the continuous function on the closed interval a, b. Numerical examples are given to show the effectiveness.