Limit cycles in state-space pipelined scattered look-ahead filters

Limit cycles of various pipelined scattered look ahead (SLA) filters are analyzed. Regions free of overflow limit cycles using two's complement arithmetic are obtained in both parameter space and in the z-domain for SLA filters. Results for zero-input quantization limit cycle stability using two's complement truncation and rounding are extended to direct form (DF) SLA filters. Combining these results. the region of global asymptotic stability from zero-input limit cycles of DF SLA filters is found. 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 and coefficient quantization noise. DF and minimum roundoff noise based structures are compared for the purpose of reducing complexity or improving numerical performance.<
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