Determination of all existing limit cycles in high-order cascade and parallel-structures of recursive digital filters

A method for the determination of limit cycles in high-order cascade or parallel structures of recursive digital filters is presented. Based on the theory for the limit-cycle analysis of second-order recursive systems for the case of common but periodic input signals, these methods are extended to high-order cascade or parallel forms built up for second-order sections. Three examples show the usefulness of the method compared to other known limit-cycle testing methods. The examples demonstrate the great influence of ordering in cascade-structures on the limit-cycle behavior