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.