全相位半带滤波器设计与实现

半带滤波器是一种特殊的低通FIR滤波器，在信号的分析与完全重构中应用广泛。本文在分析全相位滤波器频率取样特性基础上，首先得到无窗、单窗全相位恒通过而双窗则低于频率取样点的结论，其次利用全相位双边带对称传输特性H设计三种类型的半带滤波器且均具有严格零相位特性，类型I和II具有实系数单位冲激响应，类型III则具有复系数冲激响应而使半频点处幅值不等于0.5。第三，分别实现全相位九种半带滤波器并与三种传统设计方法进行比较，结果表明，全相位设计半带滤波器通带及阻带波纹数更少，且衰减降低近3dB。 

Design and Implementation of All-phase Half band Filter

Half band filer is a kind of special filter which is widely used in analyzing and synthesizing digital signals. In this paper, frequency sampling property of all-phase filter is firstly discussed to arrive at that none and single windowed all-phase filter accurately pass the sampling pointes, whereas the dual-windowed always rises just below. Secondly, three kinds of all-phase half band filters are proposed according to the bi-symmetry of transmission property H . Type I and II all-phase half band filters possess real coefficients unit impulse response. However, type III possesses complex coefficients, which makes semi-frequency amplitude not equal to 0.5. Those three all-phase half band filters have linear phase. Thirdly, experiment is designed to implement 9 all-phase half band filters (none/single/dual windowed)and compared with traditional 3 methods(windowed/Lagrange/semi-band) . The result shows that this novel all-phase half band filter has much fewer ripples and lower attenuation by at least 3dB.