Design of Discrete-Valued Linear Phase FIR Filters in Cascade Form

Digital filters in cascade form enjoy many advantages over their equivalent single-stage realizations in that lower coefficient sensitivity, higher throughput, reduced computational and smaller implementation cost can be achieved. However, the numerical design and optimization of such structure are of much more difficulty than the single-stage case if the filter coefficients are restricted to be of discrete values. This is mainly due to the non-convexity of the constraints, which rules out the possibility of employing sophisticated convex optimization techniques as well as the guaranteed global optimality. In this work, a general-purpose algorithm is proposed for the design of linear phase finite impulse response (FIR) filters in cascade form with discrete coefficients. The proposed algorithm decomposes the overall filter into subfilters during the traverse of a tree search of the overall filter. Discrete-valued linear phase FIR filters are able to be searched and decomposed into both symmetric and non-symmetric subfilters. The optimization complexity is of the same order as the single-stage filter optimization. Design examples have shown that the proposed algorithm is capable of achieving notable reduction in both implementation cost and adder depth compared with their single-stage optimum designs.