关于数字滤波器与线性相位特征的讨论

Discussions on the Relationship Between Digital Filters and Linear-phase Frequency Response

针对FIR数字滤波器具有线性相位的充要条件,本文给出了必要性命题的严格证明,即证明线性相位FIR系统的单位脉冲响应必然为奇对称或偶对称,以弥补相关教材在这一问题论述的不足。论文由该证明过程进一步指出,有限阶次的因果IIR数字滤波器不可能具有线性相位。

To make up for the lack of relevant content, a strict proof is given for the necessary condition that an even symmetry or odd symmetry on the FIR digital filter coefficients guarantees a linear-phase frequency response, and from the proof a conclusion is drawn that finite-order causal stable IIR filter can not have linear-phase characteristic.