Showing papers on "Bessel filter published in 1978"

The three‐dimensional convolution of reduced Bessel functions and other functions of physical interest

Abstract: A method for evaluating convolution integrals over rather general functions is suggested, based on the analytical evaluation of convolution integrals over functions BMν,L(r) = (2/π)1/2rL+νKν (r) YML(ϑ,φ), which are products of modified Bessel functions of the second kind Kν(r), regular solid spherical harmonics rLYML(ϑ,φ), and powers rν.

On the computation of modified Bessel function ratios

Abstract: A detailed comparison is made between a continued fraction of Gauss, and one of Perron, for the evaluation of ratios of modified Bessel functions IV(x)/Ij .l(x), x > 0, v > 0. It will be shown that Perron's continued fraction has remarkable advantages over Gauss' continued fraction, particularly when x >? v.

The use of filtered Bessel functions in direct interpretation of geoelectrical soundings

Abstract: We start from the Hankel transform of Stefanescu's integral written in the convolutionintegral form suggested by Ghosh (1971). In this way it is possible to obtain the kernel function by the linear electric filter theory. Ghosh worked out the sets of filter coefficients in frequency domain and showed the very low content of high frequencies of apparent resistivity curves. Vertical soundings in the field measure a series of apparent resistivity values at a constant increment Δx of the logarithm of electrode spacing. Without loss of information we obtain the filter coefficient series by digital convolution of the Bessel function of exponential argument with sine function of the appropriate argument. With a series of forty-one values we obtain the kernel functions from the resistivity curves to an accuracy of better than 0.5%. With the digital method it is possible to calculate easily the filter coefficients for any electrode arrangement and any cut-off frequency.

Common zeros of two Bessel functions

Abstract: There is a theorem that two Bessel functions JA(x) and Jv(x) can have no common positive zeros if ,u is an integer and v = 1g + m where m is an integer, but this does not preclude the possibility that for unrestricted real positive ,u and v not differing by an integer, the two functions JA(x) and Jv(x) can have common zeros. An example is found where two such functions have two positive zeros in common.

A recursive digital filter with maximally flat linear phase at an arbitrary specified frequency

Abstract: An available recursive digital low-pass filter with constant group delay cannot be spectral transformed to give, for example, a bandpass filter which also has constant group delay. This correspondence describes a technique, using Gauss-Jordan elimination, to design a recursive digital filter with maximally flat linear phase at an arbitrary specified frequency.

Constant group delay approximation by series of Bessel polynomials

Abstract: The transfer function obtained from the tuncated expansion of exp(p) in series of Bessel polynomials yield an approximation of the ideal filter. Thanks to a freely chosen parameter, it is possible to control the compromise between optimal amplitude and phase or between the rise time and the overshoot of the step response. Compared to the classical Thomson characteristic, which is linked to a single Bessel polynomial, the delay deviation in the passband is smaller.

A generalization of Bessel's approximation and its application to model reduction

Abstract: The direct continued-fraction method for model reduction corresponds to the Pode formula. The squared magnitude continued-fraction method for stable reduced models is a modification of the direct method. We naturally think of the counterpart of the squared magnitude continued-fraction method—the tangent phase function. This paper establishes a detailed procedure for the continued-fraction expansion of the tanget phase function. It turns out that the procedure is a generalization of the Bessel filter approximation. Therefore, new light has been shed on the classical filter problem. Two demonstrative examples—a pitch rate control of a supersonic transport aircraft and a pupil reflex system—are included.