近Nyquist频率情况下的数字化陷波器设计方法研究

Research on Design Method of Digital Notch Filter When Notch Frequency Approaching Nyquist Frequency

为解决陷波中心频率接近Nyquist频率时常规离散化方法引起的陷波滤波器性能退化问题,提出一种改进的零极点匹配离散化方法。通过修正连续域滤波器的阻尼比至一个受约束的期望值,使离散化后的结构滤波器的频率特性和连续域设计结果一致。通过计算机数值计算解特定的约束不等式,获得了期望阻尼比的数值解,避免了求解复杂超越方程的困难。通过数字仿真,验证了弹体弹性模态频率摄动情况下的数字滤波器性能。仿真结果表明,改进零极点匹配离散化的方法有效消除了近Nyquist频率情况下现有离散化方法的缺点。

A modified pole-zero matched discretization method is peresented for overcoming performance degradation of the notch filter discreted by currently popular methods when the notch frequency approaching the Nyquist frequency.The frequency characteristic of the discreted notch filter is kept up with that of notch filter in continuous domain by modifying damping ratio of transfer function in continuous domain to a constrained expectation.The numerical solution is obtained by solving a specified constraint equation and the difficulty of solving complex transcendental equation is avoided.The performance of digital notch filter is tested in digital simulation with conditions that the notch frequency with limited uncertainties.The simulation results show that the modified pole-zero matched discretization method presented in this paper is valid to overcome the drawback of currently popular discretization methods when the notch frequency approaching the Nyquist frequency.