The Delta Modulation has step size much smaller after quantization and also the sampling rate is much higher.

**Features** of Delta Modulation

- It is of moderate quality
- The modulator and demodulator have simple designs.
- There is an approximation of the staircase waveform.
- The user can decide the bit rate.
- Its implementation is simpler.

The Delta Modulation is also called 1-bit DPCM because it is the simplified form of DPCM. The signal correlation is higher as the sampling interval is less.

**Delta Modulator**

There are two summer circuits, a delay unit and also a 1-bit quantizer in the Delta Modulator circuit. The block diagram is as shown

In DM just a single delay unit is used unlike the predictor unit in the DPCM modulation technique. The notations used in above figure are described here as

- x (n T
_{s})= over sampled input - e
_{p}(n T_{s}) = summer output and quantizer input - e
_{q}(n T_{s}) = quantizer output = v (n T_{s}) - xˆ (n T
_{s}) = output of delay circuit - u (n T
_{s}) = input of delay circuit

The process of delta modulation is understood using the above mentioned notations

e_{p}(nT_{s})=x(nTs)−xˆ(nTs) ———equation 1

=x(nTs)−u([n−1] Ts

=x(nTs)−[xˆ[[n−1] Ts] +v[[n−1] Ts]] ——-equation 2

Also,

v(nTs)=eq(nTs)=S.sig. [ep(nTs)] ———equation 3

u(nTs)=xˆ(nTs)+eq(nTs)

Where,

xˆ(nTs) = the previous value of the delay circuit

eq(nTs) = quantizer output = v(nTs)

Hence,

u(nT_{s})=u([n−1] T_{s}) +v(nT_{s})———equation 4

Which means,

**The value of present input of the delay unit will be**

**= **The previous output of the delay unit **+ **the present quantizer output the present quantizer output

We here assume that there is zero condition of Accumulation

The output of the delay unit is an accumulator output which is lagging just by 1 sample.

The structure of the demodulator can be calculated with the help of equation 5 and 6

The output of the delta modulator will be a staircase approximated waveform with the step size as delta (**Δ**). The quality of the output waveform is moderate.

**Delta Demodulator**

There is a delay unit, a low pass filter and a summer in the delta demodulator circuit. Since we don’t have any predictor unit so there is assumption that no input to the demodulator. The delta demodulator is below.

From the above diagram, we have the notations as −

vˆ(nT_{s}) is the input sample

uˆ(nT_{s}) is the summer output

x¯(nT_{s}) is the delayed output

The input to the demodulator is a binary sequence. The input to the low pass filter will be the staircase approximation of the output.

There are many reasons for using a LPF in the circuit but mainly we use it to remove the noise for out of band signals. The drawback in the delta modulation is granular noise which occurs due to the step size error at the transmitter. In the absence of noise both the modulator output and demodulator input are equal.

**Advantages of DM **

- It is a 1-bit quantizer
- The design of the modulator and demodulator is very simple.

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