Minimum Norm Recursive Digital Filters that Are Free of Overflow Limit Cycles

In recursive digital filters, the norm of the system matrix is an important design parameter with respect to overflow behavior. Filter realizations that minimize this norm are shown to be free of autonomous overflow limit cycles. Overflow-stable filters of any order, without any constraints on pole locations within the unit circle, can be realized by parallel-cascade structures of minimum norm systems. Minimum norm realizations require the minimum number of delay elements but, in general, more than the minimum number of multiplications and additions.