Detection and removal of LCOs in IIR filters

A finite state machine method is proposed for realizing IIR digital filters. This realization has a maximum error of 1/2 bit from the final result of infinite-precision arithmetic, and has no error growth during the processing period. It avoids the effects of the filter coefficient quantization and multiplication arithmetic errors. A connection matrix method is presented for detecting and locating the limit-cycle oscillations (LCOs). The concept of suboptimum successor based on the defined error function is introduced. A graph theory method is proposed for removing limit-cycle oscillations from digital filters. This method breaks the filter´s cycles, connects the unstable state to its suboptimum successor, and forms a tree graph of stable filters. It introduces a minimum noise increase and hardly any increase in hardware complexity