Bessel filter

About: Bessel filter is a research topic. Over the lifetime, 656 publications have been published within this topic receiving 16808 citations.

Approximation of Bessel beams with annular arrays

Abstract: It is shown that the limited-diffraction Bessel beam of order zero can be generated by a transducer with equal-area division of elements and with a fixed prefocus, i.e. conventional transducers used in medical imaging equipment. The element division implies that the scaling parameter must be chosen to contain the first lobe of the Bessel function in the first element. In addition the prefocus must be such that the array is steerable to infinite depth. Examples of low- (3.5 MHz) and high-frequency (20 MHz) arrays are shown where the approximate Bessel beam compares favorably with a spherically focused beam with a fixed focus. The main advantages are a sharper nearfield and a more uniform beamwidth.

Further comments on the computation of modified Bessel function ratios

Abstract: A theorem by W. J. Thron is used to enhance and further substantiate empirical results by Gautschi and Slavik on the convergence of continued fractions used to compute ratios of modified Bessel functions. 1. Thron's Theorem Applied to Continued Fractions for Ratios of Modified Bessel Functions. A theorem by Thron* [2] offers analytic confirmation of recent empirical results [1] on the convergence of continued fractions, cfs, for computing ratios of modified Bessel functions. Defining Thron's Theorem 6.1 states: The continued fraction K(an/1) converges to a value u which satisfies R(u) > -Vi provided that J2(an) < R(an) + % and \\an\\ 1. Here M is an arbitrary large positive quantity. As a consequence of Thron's theorem we can obtain a priori bounds on the truncation error, 2Rn, of Gauss's and Perron's cfs for modified Bessel function ratios. In the case of Thron's Theorem 6.1, Rn is the radius of the value region (nested circles within which the value of the cf lies) of the cfs. From Thron's theorem we thus have *7,<1 Üil + Ui4Mk)). I *=i Relatively larger values of M are associated with overall slower convergence. Both Gauss's and Perron's cfs for Iv(x)/Iv_x(x) are in the form required by the theorem [1]. For positive x the assumptions of Thron's theorem are trivially satisfied for Gauss's cf and are easily verified for Perron's cf if v > 1. Thus, to apply the theorem, note that when x » v, the an of Perron's cf will be dominated by l/a0{x) = x/ix + 2v) and the an of Gauss's cf will be dominated by axix) = (l/4)x2/v(v + 1), which we will refer to asMp and MG, respectively. Clearly, as* » v, Mp< 1 and MG » 1. In this case, Rn, or 2Rn (the truncation error), of Gauss's cf is much larger than Perron's, indicating slower convergence of the Gauss cf. These results are given in Table 1.1 which reproduces Table 3.2 of [1] supplemented by values of Mp and MG Received March 20, 1978; revised September 5, 1979. 1980 Mathematics Subject Classification. Primary 33A40; Secondary 40A15, 65D15. * Thron's theorem referred to here is actually a special case of an earlier result due to Scott and Wall (Trans. Amer. Math. Soc, v. 47, 1940, pp. 155-172). However, the results of this paper depend on the proof as given by Thron. © 1980 American Mathematical Society 0025-5718/80/0000-0119/$01.75 937 License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use 938 MARIETTA J. TRETTER AND G. W. WALSTER (k in Table 1.1 represents the number of terms required in the Gauss and Perron cfs to obtain relative accuracy of tëlO-8, as originally given in Table 3.2 of [1]). One interesting observation in Table 1.1 is the fact that for x » v, Mp is increasing slightly as x increases, even though the table indicates, for 8 decimal digit accuracy, that Perron's cf is converging faster with increasing x. This phenomenon is explained by looking at Figure 3.3 in [1]. The increase in Mp reflects the fact that, although initial convergence is fast, at extreme accuracies the convergence slows down before regaining speed. The phenomenon of slowing down also becomes more pronounced as x increases. Thus, one must be careful to interpret M as an overall measure of convergence. Table 1.1 Number of terms, k, required in the Gauss and Perron cfs to obtain relative accuracy of &10~ 8 (as given in Table 3.2 of [1 ] ), and M as defined above.

A Study of the Effect of Integrating Low-Pass Filter in Measuring the Dynamic Performance of a High Speed 8-bit Analog-to-Digital Converter (ADC)

Abstract: This research focuses on integrating a low pass filter to the AD7575 DUT Board to measure its dynamic performance. The DUT Board integrated with the low-pass filter was attached to the ADI Family Board and was tested using the CTS5010 resources to measure the necessary dynamic performance parameters. The low pass filter was used to lessen the out-of-bound noise going into the ADC input that affects the measurement of dynamic performance of the ADC. Three active low pass filters were designed on the circuit board, namely Butterworth, Chebyshev and Bessel Filter. The integration of the filter showed significant change, with the Butterworth filter giving better measurement as compared to the other low-pass filters used.

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.