Fixed-point-coefficient FIR filters and filter banks: Improved design by randomized quantizations

Frequency-selective, linear FIR filters are considered, as single systems and with analysis-synthesis filter banks. They are usually designed, in the single-channel case, to fulfill tolerances in the Chebychev sense, or in near-perfect-reconstruction filter banks, to minimize a reconstruction-error measure. If hardware is limited, fixed-point coefficient quantization is needed. It causes, in general, tolerance violations or a larger reconstruction error. Discrete re-optimization may help. A recent technique, able to handle also large filter orders, is successfully applied and newly extended to filter banks. Even better are randomized strategies, introduced and examined in the mathematical-optimization community over past 15 years; especially, randomized rounding is very effective. Thereby, good results are found for both single-system and filter-bank designs. We further introduce a new random sub-set selection within th above re-optimization. Like randomized rounding, it allows a trade-off between computational effort and solution quality. Clear improvements over deterministic heuristics are obtained by both randomized algorithms.