ELIMINATION OF LIMIT-CYCLES DUE TO TWOS COMPLEMENT QUANTIZATION IN NORMAL-FORM DIGITAL-FILTERS

Normal form digital filters are attractive due to their desirable prop erties 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 tru ncation (TCT) quantization is used, limit cycles can still exist. In t his paper, it is shown that when block structures are used, normal for m digital filters can be made free of limit cycles due to TCT quantiza tion. It is shown that this can be done with a small block size, An al gorithm is also presented to find the minimum block size required for a given filter. Some examples are given to illustrate the results.