Memory requirements of first-order digital filters

The authors pose the question of the memory requirements of digital filters as determined by filter parameters and desired accuracy, and present a full analysis for first-order filters. The main feature of this investigation is that lower bounds are obtained with no structural assumption on the finite-state machine selected to approximate the ideal filter. Two specific realizations are discussed, a classical state-roundoff implementation and a higher order FIR-approximation. Upper and lower bounds on memory requirements are shown to be in remarkable agreement