• To overcome the quantization errors due to slope overload and granular noise, the step size (δ) is made adaptive to variations in the input signal x(t).

• Particularly in the steep segment of the signal (t) , the step size is increased .When the input is varying slowly , the step size is reduced .Then the method is called Adaptive Delta Modulation(ADM).

• The adaptive delta modulators can take continuous changes in step size or discrete changes in step size.

• Fig 5.4.1 (a) shows the transmitter and 5.4.1 (b) shows receiver of adaptive delta modulator. The logic for step size control is added in the diagram.

• The step size increases or decreases according to certain rule depending on one bit quantizer output .For example if one bit quantizer output is high (1), then step size may be doubled for next sample.

• If one bit quantizer output is low, then the step size may be reduced by one step. Fig 5.4.2 shows the waveforms of adaptive delta modulator and sequence of bits transmitted.

• In the receiver of adaptive delta delta modulator shown in Fig 5.4.1(b) the first part generates the step size from each incoming bit. Exactly the same process is followed as that in transmitter.

• The previous input and present input decides the step size. It is then given to an accumulator which builds up staircase waveform.

• The lowpass filter then smoothens out the staircase waveform to reconstruct the smooth signal.

• Let the input signal be sinusoidal with amplitude A volts and frequency $f_m$ Hz as shown in following figure.

• Let ,the given signal is x(t)=Acos$ω_m$ t

• The slope of this signal will be maximum when derivative of x(t) with respect to time is maximum .

∴ Slopeofx(t)= dx(t)/dt= - A$ω_m$ sin$ω_m$ t

The maximum value of the slope of x(t) = -A$ω_m$………..(1)

Slope of the staircase approximated signal $x' (t) = δ/T_s $ …………..(2)

To avoid the slope overload distortion , it is necessary that the maximum slope of x(t) be less than the slope of x' (t)

This is the condition for avoiding the slope overload distortion .Therefore the slope overload distortion will occur if this condition is not satisfied i.e,

If$ A \gt\frac{δ}{ω_m T_s} $