Pipelined implementation of recursive filter

If the input to a pipeline depends on its previous output, poor hardware utilization can result because the required output is not immediately available. In a recursive filter, the output at the n th sampling instance, y(n), depends on its previous output, y(n-1). Thus, pipeline implementation of recursive filter may result in poor hardware utilization if the dependency problem is not resolved. This problem can be solved by substitution. However, unsuitable substitution can lead to instability. The stability of pipelined recursive filter is investigated, and substitution strategies that produce stable filters are presented. The use of complex conjugate pole-zero pairs is discussed, and roundoff noise is considered