高阶微分器优化设计研究

Optimum Design Study of the High-Order Differentiator

提出了一种基于BP算法的正弦基函数神经网络模型 ,研究了该数神经网络算法与线性相位微分器幅频特性的关系 ,提出了该神经网络算法的收敛条件 ,给出了高阶微分器的优化设计实例 .计算机仿真结果表明了该神经网络算法不仅是有效的而且是高效的 .与传统的窗口函数法和雷米兹化设计方法相比 ,本优化设计方法不需要计算矩阵的逆 ,因而解决了雷米兹优化设计方法求高阶矩阵逆的困难 .由于微分器是一种特殊的 4型FIR线性相位滤波器 ,只要求出脉冲响应序列 ,就可以用软件方法实现数字微发运算 ,也可以通过CPLD复杂可编程器件或DSP数字信号处理芯片实现硬件数字微分运算 ,因此 。

This paper presents an model of sine basis functions neural network based on BP algorithm, discusses the relation between the algorithm of neural network and amplitude-frequency characteristic about the linear phase differentiator, introduces the convergence condition of neural-network algorithm, and studies the optimal design example about the high-order differentiator. The simulation result shows that the neural-network algorithm is not only effective but also very good. Compared with the traditional methods of window functions and Remez optimal algorithm, the optimum design method in the paper need not compute inverse matrix, so solves the difficulty to compute high-order inverse matrix in Remez optimal design method. Because differentiator is a kind of the special type-four FIR linear phase filter, Digital differential operation may be achieved by soft method as long as the pulse response sequence is obtained. It can be done by hardware method such as CPLD of DSP. It is very significant that the excellent differentiator, especially high-order differentiator is designed in practice.