Control of limit cycles in recursive digital filters by randomized quantization

The different types of limit cycles which can occur in single second-order sections respond differently to efforts to reduce them. Length 1 (dc) limit cycles play an important complicating role, especially in cascaded filters. We describe a simple method, involving random requantization of multiplier outputs, which can reduce or eliminate limit cycles in digital filters. We compare limit cycle and roundoff noise in three typical low-pass filters with and without the method.