Short note: Adaptive delta modulation

Adaptive Delta Modulation (ADM) is a delta modulator in which the step size $\Delta$ is varied automatically according to the slope of the input signal, instead of being fixed.

Why needed: linear DM with a fixed step faces a trade-off. A large $\Delta$ avoids slope overload but gives large granular noise; a small $\Delta$ gives low granular noise but causes slope overload. ADM removes this conflict.

m(t)->(+)->[1-bit Q]-+-------------> out
      ^-             |
      |              v
      +-[Accum]<-[x]<+--[Step-size logic]
                  ^         |
                  +---------+

Working

• The output bits are watched by a step-size control logic.
• If several successive bits are the same (e.g. 111 or 000), the signal is rising/falling steeply, so the step is increased (e.g. multiplied by 1.5 or doubled).
• If the bits alternate (1010), the signal is flat, so the step is reduced (e.g. halved), down to a minimum $\Delta_{min}$.
• The receiver uses the same logic on the received bits, so no extra side information is sent.
• A common rule (Song algorithm): $\Delta_k = |\Delta_{k-1}|\left(e_k + \tfrac{1}{2}e_{k-1}\right)$; another is CVSD (continuously variable slope DM).

Advantages

• Reduced slope overload and granular noise together.
• Wider dynamic range and better SQNR than linear DM at the same bit rate.
• Good speech quality at 16–32 kbps (CVSD used in military and Bluetooth voice).

Drawback: more complex circuitry; bit errors affect step size for a few samples.