Design of Low-Delay FIR Half-Band Filters with Arbitrary Flatness and Its Application to Filter Banks

Half-band filters are a class of important filters among digital filters, and have been widely used in many applications such as filter banks and wavelets. The conventional methods are mainly concerned with FIR half-band filters with exactly linear phase. However, the exactly linear phase filters have a drawback of large group delay when high-order filters are required. In this paper, the design of FIR half-band filters with a lower group delay is considered. In some applications of filter banks and wavelets, a flat magnitude response is required for the half-band filters. Therefore, a new method for designing low-delay FIR half-band filters with arbitrary flatness is proposed. In the proposed method, while taking the specified flatness condition into account, the design problem is formulated by using the complex Remez exchange algorithm in the stopband. Then, a set of filter coefficients can be easily obtained by solving a simple system of linear equations. The optimal solution with an equiripple response in the stopband is obtained by applying an iteration process. Finally, the proposed method is applied to the design of two-channel perfect reconstruction filter banks with low group delay to demonstrate its effectiveness. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(10): 1–9, 2000