Design of IIR Half-Band Filters with Arbitrary Flatness and Its Application to Filter Banks

摘要

Half-hand filters are important for applications to multirate signal processing and wavelets. Previously, FIR half-band filters have mainly been treated. However, it should be recognized that the IIR filter can produce frequency characteristics similar to those of the FIR filter with a low order. Also, in the applications of filter banks and wavelets, design of a half-band filter is needed in which the degree of flatness can be specified arbitrarily. In the present paper, a new design method is proposed for an IIR half-band filter with an arbitrary degree of flatness. In the present design method, the analytical solution of the filter coefficients is given in the case of a maximally flat filter. Also, in the case of a specified degree of flatness, the amplitude error in the stopband can be specified in the design. Further, the stability of the filter is studied and then the minimum group delay for causal stability is clarified. Finally, the IIR half-hand filter is applied to the design of a two-channel filter bank and the effectiveness of the present design method is proven.