基于Matlab的IIR数字低通滤波器的设计方法

详细的阐述了IIR数字滤波器设计的一般步骤，首先根据给定的目标数字滤波器的性能指标，将其转换为模拟滤波器的指标参数，再根据巴特沃思（Butterworth）低通模拟滤波器的设计原理设计出相应技术指标下的模拟低通滤波器，最后采用双线性变换将设计出的模拟低通滤波器转换为数字滤波器，即得到了期望的IIR数字滤波器。针对实例，在Matlab环境下分别设计出了4阶、11阶、25阶的IIR数字滤波器，通过仿真验证了滤波器的速度与滤波效果之间不是完全的统一。最后，分析了双线性变换频率畸变现象，造成相同频率下离散后的幅值变小。通过频率预曲折方法对双线性变换进行相应的补偿。以25阶滤波器为例，仿真结果显示，在指定频率处实现了幅值在转换前后大小不变的效果。

Designing and Implementation of Lowpass IIR Digital Filter

This paper described the general steps of IIR digital filter design. Firstly, the given specifications of the digital filter were converted to those of the equivalent analog filter. Then, a low pass analog filter with the specifications was implemented according to the Butterworth low-pass analog filter designing method. Finally, the analog filter was converted to the correspondent digital filter by using bilinear transform so that the desired IIR low-pass digital filter was derived. For verification, in the MATLAB environment the 4-order, 11-order and 25-order IIR low-pass digital filters were designed and verified by simulation. The results have shown that the speed and the filtering performance cannot be balanced. Finally, the frequency distortion phenomenon of the bilinear transform was analyzed and it is demonstrated that the amplitude in the same frequency will be small after discretization. Therefore, the Prewarping method can be used to compensate the bilinear transform appropriately. Simulations of a 25-order digital filter verify the validity of the compensation effect of the frequency prewarping.