Adaptive Delta Modulation, a modification of Linear Delta Modulation (LDM) is a scheme that circumvents the deficiency of DM. In ADM step size Δ of the Quantizer  is not a constant but varies with time , we shall express Δ as $\Delta&space;(n)=&space;2&space;\delta&space;(n)$ .

where $\delta&space;(n)$ increases during a steep segment of input and decreases for a slowly varying segment of input.

The adaptive step size control which forms the basis of an ADM scheme can be classified in various ways such as

• Discrete or Continuous.
• instantaneous (or) syllabic (fairly gradual change).
• forward (or) backward.

we shall describe an adaptation scheme that is backward, instantaneous and discrete in practical implementation , the step size $\delta&space;(n)$ is constrained in between some pre-determined minimum and maximum values.

$\delta&space;_{min}&space;\leq&space;\delta&space;(n)\leq&space;\delta&space;_{max}$

The upper limit $\delta&space;_{max}$ controls the amount of Slope over load distortion and the lower limit $\delta&space;_{min}$ controls the granular noise (or) Idle noise.

The adaptive rule for  $\delta&space;(n)$can be expressed in the general form $\delta&space;(n)&space;=&space;g(n)&space;\delta&space;(n-1)$

where the time varying gain g(n) depends on the present binary output b(n) and M previous values b(n-1),b(n-2) ……….b(n-M). The algorithm is usually initiated with $\delta&space;_{min}$.

when M=1, b(n) and b(n-1) are compared to detect probable slope over load {b(n) = b(n-1)} (or) probable granularity  {b(n) ≠ b(n-1)} then g(n) is

• $g(n)&space;=&space;P$ if     $b(n)&space;=b(n-1)$.
• $g(n)=\frac{1}{P}$ if   $b(n)&space;\neq&space;b(n-1)$.

when $b(n)&space;=b(n-1)$ Slope overload distortion is detected and when $b(n)&space;\neq&space;b(n-1)$ Idle noise is detected.

where $P\geq&space;1$, note that $P=1$ represents LDM. $P_{optimum}=1.5$ minimizes the Quantization noise for speech signal, where $1<&space;P<&space;2$ is for broad class of signals.

The logic for step size control is added in the diagram the step size increases (or) decreases according to specified rule depending up on one bit Quantizer output.

for example if one bit Quantizer output is high then the step size may be doubled for next sample.

if one bit Quantizer output is low, the step size may be reduced by one step.

In the Receiver of Adaptive Delta Modulator there are two parts logic for step size and accumulator.

The first block produces the step size from each incoming bit, which uses the same principle used in the Transmitter.

The previous input and present input decides the step size. It is then applied to an accumulator, which builds up stair case wave form. The LPF then smoothens out the stair case wave form to reconstruct the original signal.