Roundoff noise minimization using delta-operator realizations (digital filters)

The authors examine the advantages of using delta operator state space realizations rather than shift operator realizations of transfer functions in terms of minimizing roundoff noise gain. They give several conditions under which the optimal roundoff noise gain for delta operator realizations is smaller than the optimal gain for shift operator realizations. They then illustrate that even sparse (and hence nonoptimal) delta operator realizations can have smaller roundoff noise gain than the optimal shift operator realizations.<>