Step Response of an Adaptive Delta Modulator

The basic concepts of delta modulation (DM) have been thoroughly discussed in several recent publications. 12 In its simpler forms, delta modulation is a method of digitally encoding an input signal X = {x,} into binary pulses C = {c,} (where each c,- = ± 1 ) so that an approximation Y = {y,} of X may be reconstructed from the pulses C by a simple decoding scheme. The signal X, although presented to the encoder as a discrete-time sequence, will normally be a sampled (and 373 perhaps digitized) version of a continuous-time analog signal. T h e encoder works by comparing each Xi with ?/,·_i through a feedback circuit to determine the sign of the subsequent pulse c,, according to the equations a = sign (xi - yi-) rrii = dMi, where Vi = Vi-1 + mi. Various forms of delta modulators differ primarily in the manner of determining the step-size Mi) of course, since only the pulses C are to be transmitted to the decoder, what is required is a rule for determining Mi from C. In conventional linear delta modulation (LDM), the step-size Mi is taken to be a constant 8, independent of the pulses C (and the signal X), so t h a t each step ra t - = ± 5 , resulting in the familiar "staircase" appearance of Y under LDM. Since in this simplest form of DM, Y can change by only 8 per step, no m a t t e r how far Xi is from i/t--i, Y has a very limited ability to keep up with X when X has a steep slope, which results in the condition known as slope overload. In contrast to LDM, adaptive delta modulation (ADM) permits M, to be modified depending on X, especially as the slope of the signal X changes.