On the sensitivity of a class of wave digital filters

The first-order sensitivity of Fettweis' wave digital filter is expressed in terms of those of its reference filter from which the wave digital filter is derived. With this explicit relation the numerically observed properties of the wave digital filter sensitivity are explained and the relation itself can be used as an efficient computing method when the sensitivities of the reference filter are available. In obtaining the above mentioned relation, the summed sensitivity invariants are used. We show that such invariants can be obtained as a consequence of impedance scaling and frequency scaling property of the reference filter.