Optimum Removal of LCOs in Digital Systems

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 growth of errors 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 in digital filters. The concept of Sub-Optimum Successor is introduced based on the defined error function. 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 sub-optimum successor, and forms a tree graph of stable filters. It introduces a minimum increase in noise and hardly any increase in complexity of hardware.