Some notes on the second-order interpolation problem of digital filters

Mullis and Roberts formulated the second-order interpolation problem of digital filters in 1976, and provided the fundamental Proposition 1 concerned with its solvability [1]. The present correspondence gives three examples which show items b) and c) of Proposition 1 provided by them are not correct. It also presents a necessary and sufficient condition of the solvability of the second-order interpolation problem.