3型FIR滤波器优化设计研究

Optimal design of the type-three FIR filter

详细研究了3型FIR线性相位滤波器的幅频响应与正弦基函数神经网络算法之间的关系,提出并证明了该模型算法的收敛性定理,给出了3型FIR带通滤波器、海尔伯特变换器和微分器的优化设计实例。研究结果表明提出的算法避免了求高价逆矩阵的困难,有效解决了3型FIR高价数字滤波器优化设计的瓶颈问题。计算机仿真结果表明了正弦基函数神经网络算法在3型FIR高价数字滤波器优化设计领域中的有效性。

The relations between the amplitude-frequency response of Type-three FIR filter with linear phase and the algorithm of neural network based on sine basic functions are studied. The convergence theorem of the neural-network algorithm is presented and proved, and the optimal design examples of the Type-three FIR band-pass filter, Hilbert convertor and differential device are given. The research shows that the algorithm presented overcomes the difficuities in computing higher-order inverse matrix, and solves efficiently the bottle-neck problem of the optimal design of Tyep-three FIR higher-order digital filters. The simulation results show that the algorithm of neural network based on sine basic functions is efficient in the field of optimal design of Type-three FIR high-order digital filters.