Elimination of limit cycles in a direct form delta operator filter

Delta operator realizations have been found to be robust against roundoff errors when high sampling rate relative to signal bandwidth is used. In this paper zero input limit cycles in the transposed direct form delta operator structure are studied. It is shown that the limit cycles of the basic delta structure are much lower in amplitude than those of the direct form delay structure for narrowband lowpass filters. Moreover, by certain modifications to the delta operator the zero input limit cycles can be completely avoided. It is also shown that narrowband lowpass filters with both low roundoff noise and absence of limit cycles can be implemented.