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...

In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained using Sinc-collocation method. This approach approximates space dimension with cardinal expansion Sinc functions. First, discretizing time derivative MRLW by classic finite difference formula, while derivatives are approximated θ—weighted scheme. For comparison purposes, we also find soliton Ad...

In our recent publications we have introduced the incomplete cosine expansion of the sinc function for efficient application in sampling [Abrarov & Quine, Appl. Math. Comput., 258 (2015) 425-435; Abrarov & Quine, J. Math. Research, 7 (2) (2015) 163-174]. Here we show that it can also be utilized as a flexible and efficient tool in mathematical analysis. In particular, an application of the inco...

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...

Oversampled functions can be evaluated using generalized sinc-series and filter functions connected with these series. A standard filter function is given by exp((ξ2 − 1)−1). We show that the Fourier transform of this filter posseses the convergence order O(exp(−√x)), improving an estimation given in [10]. Moreover, we define a family of filter functions with convergence order O(x · exp(−xσ)) w...

Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker–Kotel'nikov–Shannon (WKS) sampling restoration sum for Bernstein function classes B q π,d , q > 1, d ∈ N, when the decay rate of the sampled functions is unknown. The case of regular sampling is discussed. Extremal properties of related series of sinc functions are investigated.

Near optimality of the sinc approximation is established in a variety of spaces of functions analytic in a strip region about the real axis, each space being characterized by the decay rate of their elements (functions) in the neighborhood of the infinity.

In this paper an alternative analysis in the time domain is described and the results of the interpolation process are presented by means of functions that are based on the rule of conditional mathematical expectation and the covariance function. A comparison between the interpolation error caused by low order filters and the classic sinc(t) truncated function is also presented. When fewer samp...

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 ...