DM is done on an over sampled message signal in its basic form, DM provides a stair case approximated signal to the over sampled version of message signal.

i.e, Delta Modulation (DM) is a Modulation scheme in which an incoming message signal is over sampled (i.e, at a rate much higher than the Nyquist rate ) to purposely increase the correlation between adjacent samples of the signal. Over sampling is done to permit the use of a sample Quantizing strategy for constructing the encoded signal.

Signaling rate and Transmission Band Width are quite large in PCM. DM is used to overcome these problems in PCM .

DM transmits one bit per sample.

The process of approximation in Delta Modulation is as follows:-

The difference between the input () and the approximation () is quantized into only two levels corresponding to Positive and negative differences.

i.e, If the approximation () falls below the signal ()at any sampling epoch(the beginning of a period)output signal level is increased by .

On the other hand the approximation () lies above the signal () , output signal level is diminished by provided that the input signal does not change too rapidly from sample to sample.

it is observed that the change in stair case approximation lies with in .

This process can be illustrated in the following figure

**Delta Modulated System:- **The DM system consists of Delta Modulator and Delta Demodulator.

**Delta Modulator:- **

Mathematical equations involved in DM Transmitter are

error signal:

Present sample of the (input) sampled signal:

last sample approximation of stair case signal:

Quantized error signal( output of one-bit Quantizer):

if .

and .

encoding has to be done on the after Quantization that is when the output level is increased by from its previous quantized level, bit ‘1’ is transmitted .

similarly when output is diminished by from the previous level a ‘0’ is transmitted.

from the accumulator

where is the Quantization error.