Limit cycle behavior of pipelined recursive digital filters

The important new class of pipelined IIR filters, called scattered look-ahead (SLA) filters, is analyzed for limit cycle behavior, including both overflow and quantization limit cycles. Direct form (DF), minimum roundoff noise (MRON) form and apparent direct form (ADF) are selected as basis structures of SLA filters. The z-domain is extensively searched as a function of the number of pipelining stages for limit cycle free regions, which is transferred from analytic parameter space results. In consequence, the DF SLA structure is proved to have merits implementing high Q filters except at certain regions near the unit circle, where the structure is highly susceptible to roundoff noise (RON) and coefficient quantization noise (CQN). DF and MRON based structures are compared for the purpose of reducing complexity or improving numerical performance