In this paper we will present an approach to realize FIR filters using Chebyshev Polynomials. Chebyshev polynomials play a vital role in antenna as well as in signal processing theory. The FIR filter design has also been disscussed previously [2-10], these papers discuss approximation methods, while the approach we will discuss in this paper gives exact design of FIR filter in Chebyshev sense. ...

This paper analyses a Chebyshev pseudospectral collocation semidiscrete (continuous in time) discretization of a variable coefficient parabolic problem. Optimal stability and convergence estimates are given. The analysis is based on an approximation property concerning the GaussLobatto-Chebyshev interpolation operator.

In the present paper we give a characterization of Chebyshev subspaces in the space of (real or complex) continuously-differentiable functions of two variables. We also discuss various applications of the characterization theorem. Introduction. One of the central problems in approximation theory consists in determining the best approximation; that is, in a normed linear space X with a prescribe...

We construct an hyperinterpolation formula of degree n in the three-dimensional cube, by using the numerical cubature formula for the product Chebyshev measure given by the product of a (near) minimal formula in the square with Gauss-Chebyshev-Lobatto quadrature. The underlying function is sampled at N ∼ n/2 points, whereas the hyperinterpolation polynomial is determined by its (n + 1)(n + 2)(n...

In paper [4], transformation matrices mapping the Legendre and Bernstein forms of a polynomial of degree n into each other are derived and examined. In this paper, we derive a matrix of transformation of Chebyshev polynomials of the first kind into Bernstein polynomials and vice versa. We also study the stability of these linear maps and show that the Chebyshev–Bernstein basis conversion is rem...

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by...

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are appro...

We exhibit a numerical technique based on Newton’s method for finding all the roots of Legendre and Chebyshev polynomials, which execute less iterations than the standard Newton’s method and whose results can be compared with those for Chebyshev polynomials roots, for which exists a well known analytical formula. Our algorithm guarantees at least nine decimal correct ciphers in the worst case, ...