Step Response of an Adaptive Delta Modulator

N. S. Jayant has proposed a simple but effective form of adaptive delta modulation which uses two positive parameters, P and Q, to adjust the step size. The values P = Q = 1 describe linear delta modulation (LDM), and Jayant has recommended using Q = 1/P and 1nQ > 1, it converges to the new level when PnQnQ = 1, it eventually settles into a periodic (2n + 2)-step cycle, for almost all initial conditions. For P ≧ 2, and for some combinations of P and Q with P between 1.6 and 2, it is possible to have both PQnQ ≧ 1, so that PQn.