Design of limit-cycle-free recursive transfer functions for fixed-point direct form implementation

An approach for the design of limit-cycle-free digital fixed-point filters is proposed. By constraining the transfer function already in the design phase, it is guaranteed that the filter will be free from limit cycles and overflow oscillations in the direct form implementation. The design strategy also guarantees low roundoff noise. The proposed approach is illustrated with design examples. The examples show that typically a 50-100% increase in the filter order (as compared to standard elliptic design) is needed for the limit-cycle-free implementation of a lowpass filter with the direct form (DF) structure. Since the DF structure is very efficient to implement in signal processors, the proposed filters are very attractive for such environment, whereas dedicated filter structures (wave digital, state-space, etc.) easily result in a 3 to 4-fold implementation complexity.<>