In this paper, we show the application of Chebyshev structure proposed by McClellan and Chan for design of three-dimensional (3-D) filters based on the McClellan transformation. We consider the implementation of 3-D FIR cone-shaped filters designed recently by Mollova and Mecklenbräuker. The Chebyshev structure is originally developed for 2-D digital filters designed by transformation method, b...

We study the rate-distortion relationship in the set of permutations endowed with the Kendall τ-metric and the Chebyshev metric. Our study is motivated by the application of permutation rate-distortion to the average-case and worst-case analysis of algorithms for ranking with incomplete information and approximate sorting algorithms. For the Kendall τ-metric we provide bounds for small, medium,...

In this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which will be used to convert the system of integral equations into a system of algebraic equations. Also, the error is analyzed and ...

In this paper we compare Krylov subspace methods with Chebyshev series expansion for approximating the matrix exponential operator on large, sparse, symmetric matrices. Experimental results upon negative-definite matrices with very large size, arising from (2D and 3D) FE and FD spatial discretization of linear parabolic PDEs, demonstrate that the Chebyshev method can be an effective alternative...

In this paper we describe the use of multivariate Chebyshev polynomials in computing spectral derivations and Clenshaw–Curtis type quadratures. The multivariate Chebyshev polynomials give a spectrally accurate approximation of smooth multivariate functions. In particular we investigate polynomials derived from the A2 root system. We provide analytic formulas for the gradient and integral of A2 ...

The effect of Window Parameter () in Dolph-Chebyshev window on the SNR of radar returns is discussed and proposed an optimum value of “” with which data may be weighed using Dolph-Chebyshev window. It is observed that the Dolph-Chebyshev window can be used with “”corresponding to the minimum of sidelobe attenuation of 50dB to taper the data for spectral analysis. From the results, it may be ...

An O(N(logN)2/ loglogN) algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equallyspaced points in the frequency domain. Both components are based on the FFT, and as an intermediate...

Let G be a strict RS-set (resp. an RS-set) in X and let F be a bounded (resp. totally bounded) subset of X satisfying rG(F )> rX(F ), where rG(F ) is the restricted Chebyshev radius of F with respect to G. It is shown that the restricted Chebyshev center of F with respect to G is strongly unique in the case when X is a real Banach space, and that, under some additional convexity assumptions, th...

Moment functions are widely used in image analysis as feature descriptors. Compared to geometric moments, orthogonal moments have become more popular in image analysis for their better representation capabilities. In comparison to continuous orthogonal moments discrete orthogonal moments provide a more accurate description of the image features. This paper compares the performance of discrete o...

In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonoverlapping multisplitting iterative method for the linear systems when the coefficient matrix is either an H-matrix or a symmetric positive definite matrix. First, m parallel iterations are implemented in m different processors. Second, based on l1-norm or l2-norm, the m optimization models are parallelly treat...