Bessel filter

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

Microcontroller based closed-loop control of a 2D quasi-static/resonant microscanner with on-chip piezo-resistive sensor feedback

Abstract: In this paper we present a 2D raster scanning quasi-static/resonant micro mirror being controlled in both axes in closed-loop with on-chip piezo-resistive sensor feedback. While the resonant axis oscillates with a given frequency, the quasi-static axis allows static as well as dynamic deflection up to its eigenfrequency because of its staggered vertical comb (SVC) drive arrangement. Due to the high quality factor of the very low damped spring-masssystem, an adapted trajectory planning using jerk limitation is applied for the quasi-static axis [1]. Nevertheless, inaccuracies of the applied nonlinear micro mirror model and external disturbances lead to undesired residual oscillation in open-loop control mode. To achieve high precise and fast beam positioning, we implement a flatness-based control algorithm with feedback to on-chip piezo-resistive deflection sensors. In comparison to previous work [2, 3], we developed a micro controller setup for driving the microscanner, that is equipped with an analog Bessel filter increasing the sensor signal quality significantly. In this study we demonstrate a small size and low power micro mirror driver including high-voltage generation and a microcontroller for real-time control as well as a head circuit board for high resolution sensing. We discuss experimental results of open-loop and closed-loop control for 2D raster scanning operation. Finally, the outlook is given to the intrinsic capability to compensate temperature drifts influencing the piezo-resistive sensor signal.

Explicit solutions to fractional differential equations via generalized gamma convolution

Abstract: In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional diffusion equations involving the adjoint operators of a square Bessel process and a Bessel process

On Temme's Algorithm for the Modified Bessel Function of the Third Kind

Abstract: Some modlficatmns to Temme's algorithm for the evaluation of the modified Bessel functmn of the third kind have been made Temme evaluates K,(x) and K,+dx) for x > 1 and ]~1 --1⁄2 from auxdmry functmns k(,(x) and kdx), which he determines by Miller's backward recurrence algorithm In this paper the starting order for the backward recurrence algorithm for ko(x) and k~(x) is given by a pmcewlse linear functmn of 1/x Also, we have found that ~t is more efficmnt, for small values of x, to calculate only kdx)/ko(x), whmh can be used with the values L(x) and L÷dx) and the Wronskian to obtam K,.(x) and K,+dx)