Showing papers on "Bessel filter published in 1984"
17 citations
01 Jan 1984
TL;DR: The Bessel type polynomials considered in this article are orthogonal with respect to the weight function obtained from the (unknown) classical Bessel weight function on R by adding a scalar multiple of the Dirac delta function at 0.
Abstract: The Bessel type polynomials considered are orthogonal with respect to the weight function obtained from the (unknown) classical Bessel weight function on R by adding a scalar multiple of the Dirac delta function at 0. The Bessel type polynomials are expressed in terms of the classical Bessel polynomials and as a 3F1 hypergeometric series. A second order differential equation with polynomial coefficients for the Bessel type polynomials is given.
12 citations
IBM1
TL;DR: In this article, the generalized Coulomb functions and their derivatives are discussed in the context of phase integral formalism, with emphasis on obtaining accurate values when the argument x is inside the classical turning point x λ, and an explicit formula for the integrand of the phase integral is presented for spherical Bessel functions.
9 citations
TL;DR: A correct expression for expanding cylindrical Bessel functions in terms of spherical harmonics is derived in this paper, since the available expression for this function is in error, which is the first correct expression in the literature.
Abstract: A correct expression for expanding cylindrical Bessel function of the first kind in terms of spherical harmonics is derived in this communication, since the available expression for this is in error.
6 citations
TL;DR: In a latter publication, the same authors have published the correct result for D,(K) and these new values should be used to evaluate the signal-to-noise ratio improvements in the paper’.
Abstract: ( 2) independent of y. This error stems from the incorrectness of (47) in the paper,’ which is valid for Bessel functions of the first kind [ 11 and not for the modified Bessel functions. Thus, the accuracy of the results plotted in the paper’ is questionable. In a latter publication [2], the same authors have published the correct result for D,(K). These new values for D,(K) should be used to evaluate the signal-to-noise ratio improvements in the paper’.
TL;DR: The associated Bessel function and its recurrence formulas are shown in this article, where they are expressed by the first kind of Hankel and spherical Hankel functions, and they can be expressed as a finite combination of exponential and trigonometric functions.
Abstract: The associated Bessel function and its recurrence formulas are shown in this article. The associated Bessel functions are expressed by the first kind of Hankel and spherical Hankel functions. It is shown that associated Bessel functions (both real and imaginary part) can be expressed as a finite combination of exponential and trigonometric functions. Moreover, cylindrical Bessel functions can be defined by associated spherical Bessel functions as given in this article. Higher orders of functions can be obtained from recurrence formulas.
Patent•
09 Aug 1984TL;DR: In this article, a low-pass filter consisting of a transverse filter and an attenuation-free resonator is proposed for the transmission of television signals. But this filter is not suitable for high-frequency signals.
Abstract: The low-pass filter indicated contains delay elements, multipliers and summers. The delay line contains two delay components, balanced with respect to the centre tap, with the delay time T and, in the more distant area, delay components with the delay time 2T. The low-pass filter comprises the cascade connection of a transverse filter and an attenuation-free resonator. The digital multipliers can be designed in a manner known per se by means of shift circuits. The special circuit provides a digital broadband low-pass filter in which the pass band and stop band are equally broad. It can be used in particular in the transmission of television signals.
TL;DR: In this article, the design of a coupling network between a prescribed RLC load and a given resistive generator over a finite frequency band to achieve the Bessel transducer power-gain characteristic of arbitrary order is discussed.
Abstract: This paper is concerned with the design of a coupling network between a prescribed RLC load and a given resistive generator over a finite frequency band to achieve the Bessel transducer power-gain characteristic of arbitrary order.
TL;DR: In this paper, a technique for obtaining the coefficients of an nth-order digital filter which has maximally flat group delay for frequencies approaching zero and which has only poles in the z−1 domain is presented.
Abstract: A technique is presented for obtaining the coefficients of an nth-order digital filter which has maximally flat group delay for frequencies approaching zero and which has only poles in the z−1 domain. The absence of zeros can considerably simplify the implementation of the filter