Limit cycles and correlated noise in digital filters

The phenomenon of highly correlated limit cycle oscillations in recursive digital filters is discussed, as well as development of the theory on which it is based. Attention is given to zero-input limit cycles that occur due to quantification of first and second order recursive digital filters and magnetitude truncation, together with rounding errors, in second order filters. It has been shown that dead band zero-input limit cycles always result when the filter relaxes from an initial condition when rounding, as opposed to no such limit cycles when truncating. A discrepancy error is usually found between the response of the finite precision version and the finite version, and it is shown to be bounded by the same formulas which were developed for zero-input limit cycles.