Analysis of limit cycles in the direct form delta operator structure by computer-aided test

Delta operator filter structures have received interest due to good roundoff noise and coefficient sensitivity properties. However, it has been reported that delta realizations may produce limit cycles. In this paper, limit cycle problem in the direct form delta operator structure is studied by using a computer-aided test. The test determines exact amplitude and period of the maximum amplitude limit cycle, including the case where the limit cycles are absent. Using this knowledge the required wordlength to satisfy limit cycle performance specifications can be accurately determined. It is shown that with narrowband lowpass filters limit cycles, if they exist, are of much smaller amplitude than those of the traditional delay realized direct form structure.