ABSTRACT

In this paper, new designs of infinite impulse response digital integrators are presented. Transfer functions of the digital integrators are derived after utilising the concept of multirate technique in the fractional interpolation of the rectangular and bilinear transform. Thereafter, the unknown variables of the obtained generalised transfer functions are optimised by using the optimisation algorithm. This yields the mean relative magnitude error, $-63.439$ dB and $-78.771$ dB for the first- and second-order, respectively. Furthermore, new designs of the first- and second-order digital differentiators are obtained by inverting the generalised transfer functions of the proposed integrator designs followed by optimisation of the unknown variables. The mean relative magnitude errors for first- and second-order differentiators are obtained as $-56.478$ dB and $-75.095$ dB, respectively. The proposed designs of integrators and differentiators exhibit the precise approximation of the ideal integrator and differentiator over the full Nyquist interval.

摘要

在本文中，提出了无限脉冲响应数字积分器的新设计。数字积分器的传递函数是在矩形和双线性变换的分数插值中利用多速率技术的概念后导出的。之后，利用优化算法对得到的广义传递函数的未知变量进行优化。这产生平均相对幅度误差，$-63.439$ 分贝和 $-78.771$分别为一阶和二阶 dB。此外，一阶和二阶数字微分器的新设计是通过反转所提出的积分器设计的广义传递函数，然后优化未知变量来获得的。一阶和二阶微分器的平均相对幅度误差为$-56.478$ 分贝和 $-75.095$分贝，分别。积分器和微分器的建议设计在整个奈奎斯特区间内表现出理想积分器和微分器的精确近似值。