New second-order digital filter sections without limit cycles

Limit cycles in recursive digital filters can be avoided along various ways. Wave digital filtering (WDF) and controlled rounding are two deterministic limit-cycle suppressing tools that are in current use. In this paper two novel second-order sections are derived from the foregoing principles that use only one quantizer with a magnitude truncation characteristic. Limit-cycle suppression in these sections applies to a broader class of input signals than in previous solutions: stability is guaranteed for the zero-input, constant-input, and alternating-input situation. More generally, all periodic excitations with periods not longer than two are admitted. As a characteristic feature the new sections contain loops which do not require quantization, because only multiplications with integer factors are involved.