Control of limit cycle oscillations in second-order recursive digital filters using constrained random quantization

Limit cycles occur in recursive digital filters due to quantization of fixed point products. A common method of preventing these limit cycles from degrading the performance of the filter is to increase the internal wordlength of the filter beyond the input encoding accuracy, increasing the cost of the filter. This paper proposes two techniques which suppress limit cycles. One involves constrained random quantization of the output of the B2multiplier of a standard second-order digital filter section. A second technique detects and eliminates dc and half sampling rate limit cycles. These techniques control all kinds of limit cycles produced by recursive filters with zero input, at the cost of a modest increase in circuit complexity.