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In this paper we propose a class of 2D circularly-symmetric filter banks based on a 1D IIR Gaussian prototype. We approach two cases, namely dyadic and uniform filter banks. The Gaussian prototype is obtained using an efficient rational approximation, namely the Chebyshev-Padé approximation. Then, using a frequency transformation, the corresponding 2D filters with circular symmetry are derived....

This paper presents a constructive method to (sub)optimal finite impulse response (FIR) approximation of a given infinite impulse response (IIR) model. The method minimizes the Hankel norm of approximation error by using the explicit solution of norm−preserve dilation problem. It has the advantage over the existing methods that it provides an explicitly constructive solution and allows the trad...

In this paper, we are going to solve a class of ordinary differential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the first kind, then we solve the ordinary differential equations by using the Adomian decomposition method

A new method is presented for near-best approximation of a real function F on [-r, r] by a polynomial of degree m. The method is derived by transplanting the given problem to the unit disk, then applying the Carath6odory-Fej6r theorem. The resulting near-best approximation is constructed from the principal eigenvalue and eigenvector of a Hankel matrix of Chebyshev coefficients of F. It is well ...

We analyze the Legendre and Chebyshev spectral Galerkin semidiscretizations of a one dimensional homogeneous parabolic problem with nonconstant coefficients. We present error estimates for both smooth and nonsmooth data. In the Chebyshev case a limit in the order of approximation is established. On the contrary, in the Legendre case we find an arbitrary high order of convegence.

This paper concerns the iterative solution of the linear system arising from the Chebyshev–collocation approximation of second-order elliptic equations and presents an optimal multigrid preconditioner based on alternating line Gauss–Seidel smoothers for the corresponding stiffness matrix of bilinear finite elements on the Chebyshev–Gauss–Lobatto grid.  2000 IMACS. Published by Elsevier Science...

In this paper, an Adomian decomposition method using Chebyshev orthogonal polynomials is proposed to solve a well-known class of weakly singular Volterra integral equations. Comparison with the collocation method using polynomial spline approximation with Legendre Radau points reveals that the Adomian decomposition method using Chebyshev orthogonal polynomials is of high accuracy and reduces th...