Delta modulation and Demodulation

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 f_{s}> 2f_{m}) 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 (x[nT_{s}]) and the approximation (x[(n-1)T_{s}]) is quantized into only two levels \pm \Delta corresponding to Positive and negative differences.

i.e, If the approximation  (x[(n-1)T_{s}]) falls below the signal (x[nT_{s}])at any sampling epoch(the beginning of a period)output signal level is increased by \Delta.

On the other hand the approximation   (x[(n-1)T_{s}]) lies above the signal (x[nT_{s}]) , output signal level is diminished by \Delta 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  \pm \Delta .

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: e[nT_{s}]=x[nT_{s}]-x_{q}[(n-1)T_{s}]

Present sample of the (input) sampled signal: x[nT_{s}]

last sample approximation of stair case signal: x_{q}[(n-1)T_{s}]

Quantized  error signal( output of one-bit Quantizer): e_{q}[nT_{s}]

if         x[nT_{s}]\geq x_{q}[(n-1)T_{s}] \Rightarrow e_{q}[nT_{s}] = \Delta.

and  x[nT_{s}]< x_{q}[(n-1)T_{s}] \Rightarrow e_{q}[nT_{s}] = -\Delta.

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

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

from the accumulator x_{q}[nT_{s}]=x_{q}[(n-1)T_{s}]+ e_{q}[nT_{s}]

                                               e_{q}[nT_{s}]=e[nT_{s}]+ q[nT_{s}]

where q[nT_{s}] is the Quantization error.

 

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Author: Lakshmi Prasanna Ponnala

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.