Each entry in List II is the defining feature of exactly one system, so the matching is direct: a-iii, b-i, c-ii, d-iv — option 4.

Slope overload — the characteristic defect of delta modulation. DM transmits one bit per sample, moving its staircase approximation up or down by a fixed step \(\Delta\) at each clock instant. The fastest the staircase can climb is therefore

\(\dfrac{\Delta}{T_{s}}=\Delta f_{s}\)

and if the input rises faster than this the approximation falls behind and cannot catch up until the input slows. The condition for avoiding it is

\(\Delta f_{s}\ge\left|\dfrac{dm(t)}{dt}\right|_{max}=A\omega_{m}\)

The opposite fault, granular noise, appears when the step is too large for a slowly varying input, so the staircase hunts about it. Adaptive delta modulation varies the step size to escape both — which is exactly what the fixed step of plain DM cannot do.

Encoding is what makes PCM digital. Sampling and quantising alone give PAM levels; the encoder turns each level into an n-bit word, and it is that step which buys regeneration and noise immunity.

The commutator is the classic picture of time-division multiplexing: a rotating switch that touches each channel in turn, giving every one its own time slot, with a matching de-commutator at the receiver kept in step by frame synchronisation. Contrast frequency-division multiplexing, where all channels are present at once but in different frequency bands.

Constant carrier frequency distinguishes AM from the angle-modulation family: in AM the envelope carries the message and the frequency stays put; in FM and PM the amplitude stays put and the frequency or phase carries the message.

Hence, the correct match is a-iii, b-i, c-ii, d-iv.