Elimination of limit cycles due to two's complement quantization in normal form digital filters

Normal form digital filters are attractive due to their desirable properties when implemented in finite wordlength arithmetic. These filters are free from all overflow limit cycles and quantization limit cycles when magnitude truncation is used. However, when two's complement truncation (TCT) quantization is used, limit cycles can still exist. In this paper, it is shown that when block structures are used, normal form digital filters can be made free of limit cycles due to TCT quantization. It is shown that this can be done with a small block size. An algorithm is also presented to find the minimum block size required for a given filter. Some examples are given to illustrate the results.