Elimination of limit cycles in floating-point recursive digital filters with error feedback

A sufficient criterion for the absence of zero-input limit cycles in recursive floating-point direct form filters is presented. Both the unlimited exponent range and underflow limit cycles are considered. For the case that the underflow limit cycles are not eliminated, an RMS bound is given. It is shown that the limit cycle behaviour of the filter is directly related to the maximum gain of the error transfer function. Error feedback can be used to shape the transfer function either to eliminate limit cycles completely or to reduce their amplitudes. The application of error feedback seems particularly attractive for short-wordlength implementations