Suppression of Limit Cycles in Digital Filters

Abstract

The injection of randan dither to suppress limit cycle oscillations in second-order direct form digital filter sections is discussed. Three types of dither signal are used: uniformly distributed random dither, binary randan dither and bandstop dither. All the limit cycles in the second-order filter sections can be suppressed by the injection of any one of three dither signals. No remaining noise appears in the output from the filter in the zero-input condition. Experimental comparisons are made of the average time taken to suppress limit cycles and of the increase in output noise caused by the dither. With binary random dither, the time to suppress a limit cycle is comparable with the time for zero-input response ofa linear filter to decay below the quantization threshold. Bandstop dither has the advantage to suppress limit cycles about as quickly as binary dither yet it causes an increase in output noise of lessthan 2 GB.