Comparative study of recursive digital filters using z and δ operators

This paper presents a comparative study of recursive digital filters based on z (shift) and δ (delta) operators. The effects of different parameters on the performance of filters are studied including coefficient quantisation, filter order, oversampling ratio and filter approximation. The capabilities and limitations of the δ operator in comparison with z are illustrated through simulation examples. This study produces some general guidelines which can be useful in selecting an appropriate operator for a particular filter specification