Adaptive Delta Modulation:
Step size is not constant.
Rather when the slope over load occurs the step size becomes progressive larger and ∴ x(+) will catch up with x(+) more rapidly.
The step size is adaptive as per level of i/p signal.
If compared with linear delta modulator, then you will find that except for the counter being replaced by digital processor, removing blocks are identical.
And $S_o (t)=-1 if x(t) \lt x’(t)$ just before kth clock edge.
Then step size at sampling instant k is :-
$S(k) = [δ(k-1)] S_o (k)+δ S_o (k-1)$
Eg : -
$k-1=5 \\ δ (k-1)= δ (5) = δ \\ δ(k-1)=δ(5)= +1$
Substituting : $- δ (6) = δ + δ = 2 δ$
∴ step size of 6th clock edge $= 2 δ%\$
Slope overload error reduced
ADM signal 1st converted into a DM signal with help of step size control logic and then applied to DM receiver.
AT o/p of low pass filter we get original signal.