We establish a relation between quadrature formulas on the interval [âˆ’1, 1], that approximate integrals of the form JÎ¼(F ) = âˆ« 1 âˆ’1 F (x)Î¼(x)dx, and SzegÅ‘ quadrature formulas on the unit circle thatâ€¦ (More)

and we assume Î±âˆ’j = Î±j, and Ï‰âˆ’j = âˆ’Ï‰j âˆˆ (0, Ï€) for j = 1, 2, . . . , I. The constants Î±j represent amplitudes, the quantities Ï‰j are frequencies, and m is discrete time. The frequency analysisâ€¦ (More)

In this paper, the algebraic construction of quadrature formulas for weighted periodic integrals is revised. For this purpose, two classical papers ([10] and [14]) in the literature are revisited andâ€¦ (More)

In this paper we are concerned with the estimation of integrals on the unit circle of the form âˆ« 2Ï€ 0 f(eiÎ¸)Ï‰(Î¸)dÎ¸ by means of the so-called SzegÃ¶ quadrature formulas, i.e., formulas of the type âˆ‘nâ€¦ (More)

Abstract. A series of papers have treated the frequency analysis problem by studying the zeros of orthogonal polynomials on the unit circle with respect to measures determined by observations of theâ€¦ (More)

This paper is concerned with rational SzegÅ‘ quadrature formulas to approximate integrals of the form IÎ¼(f) = âˆ« Ï€ âˆ’Ï€ f(e )dÎ¼(Î¸) by a formula like In(f) = âˆ‘n k=1 Î»kf(zk) where the weights Î»k areâ€¦ (More)