# Differential Pulse Code Modulation (DPCM)

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In this article we explained all main and important points regarding Differential Pulse Code Modulation (DPCM) in detail.

let’s understand the topic:

In PCM (Pulse code modulation) It is observed that, the adjacent samples of a signal are highly correlated with each other. So, the adjacent sampled valued signal does not much change.  Which means , present sampled value to next sampled value does not vary by a large amount. It means, the adjacent samples of the signal carry the same information with a small difference.

Read more: Pulse Code Modulation (PCM)

Sampling Theorem

The adjacent samples of the signal carry lots of redundant information. If these samples are encoded by a Standard PCM system, the resulting encoded signal contains some redundant bits (redundant information).

Figure 1 below shows a continuous time signal x(t) by dotted line. This signal is sampled by flat top sampling at regular time intervals T, 2T, 3T …..  nTs .

Here, sampling frequency is selected in such a way, it is higher than the Nyquist rate. These samples are encoded by using 3-bit (7 levels) PCM. In figure 1, small circles shown the quantized value of samples to the nearest digital level. On the top of the each samples encoded binary value is written. Here we see in figure 1, that the samples taken at 4T, 5T and 6Tare encoded to same value of (110). This information can be carried only by one sample value. But three samples are carrying the same information means redundant.

Now, consider another example of samples taken at 9Ts and 10Ts time interval. The difference between these samples only due to last bit and first two bits are redundant, since they do not change. If this redundancy is reduced, then overall bit rate will decrease and number of bits required to transmit one sample will also be reduced. This is obtained by a digital pulse modulation technique is called as Differential PCM (DPCM) technique.

## Working Principle of Differential pulse code modulation (DPCM)

DPCM works on the principle of prediction. The present sampled value is predicted from the past sampled value. The predicted value may not be exact, but it is very near to the actual sampled value.

Working of DPCM is explained with the help of block diagram of DPCM transmitter section and DPCM receiver section.

## Differential pulse code modulation (DPCM) Transmitter

Figure 2 given below shows the block diagram of DPCM transmitter section.

The main components of DPCM transmitter are comparator, quantizer, prediction filter, and an encoder.

Let x(t) be the signal to be sampled and x(nTs) be its samples. The predicted signal is indicated by x^(nTs). Now x(nTs) sampled signal and x^(nTs) predicted signal is given to the comparator. The comparator in the transmitter, finds out the difference between the actual sample value x(nTs) and predicted sample value xˆ(nTs). The output of comparator is called error signal and it is denoted by e(nTs).

The output of comparator is given by,

e(nTs) = x(nTs) – xˆ(nTs)……………………….(1)

The predicted sample value xˆ(nTs) is produced by using a prediction filter.

Now, the output of comparator e(nTs) is given to the quantizer.

Quantizer output,

eq(nTs) = Q[e(nTs)] = e(nTs) + q(nTs) ……………………..(2)

The quantizer output signal eq(nTs) is called quantized error signal eq(nTs).

By encoding the quantizer output, in this method, we obtain a modified version of the PCM called differential pulse code modulation (DPCM).

Now, to makes the prediction more and more close to the actual sampled signal. The quantizer error signal eq(nTs) and the previous prediction is added and given as input to the prediction filter, this signal is denoted by xq(nTs).

Predictor input is the sum of quantizer output eq(nTs) and predictor output xˆ(nTs)

xq(nTs) = xˆ(nTs) +  eq(nTs)……………………..(3)

Now, put the value of  eq(nTs) from eq.(2)  in the above eq. (3) , we get,

xq(nTs) = xˆ(nTs) +  e(nTs) + q(nTs) ………………….(4)

So, the equation (1) is written as,

e(nTs) = x(nTs) – xˆ(nTs)

we get x(nTs) from the above equation

x(nTs) = e(nTs)  +  xˆ(nTs)

by putting the value of  e(nTs)  +  xˆ(nTs) from the above equation into equation 4, we get,

xq(nTs) = x(nTs) + q(nTs) …………………..(5)

From equation (5) we can say that, the input of the predictor xq(nTs) is the sum of original sample value x(nTs) and quantized error q(nTs).

Figure 3 given below shows the block diagram of DPCM receiver section.

The DPCM receiver section consists of a decoder to reconstruct the quantized error signal from incoming DPCM input signal. The decoder output eq(nTs) and predictor output xˆ(nTs) are summed up to give xq(nTs) the quantized version of the original signal. Correspondingly the receive output signal differs from the input x(nts) only by the quantizing error q(nTs).

## Advantages ofDifferential pulse code modulation(DPCM)

There are three important advantages of Differential Pulse Code Modulation technique (DPCM) are given below:

1. Reduced Bitrate: By using DPCM efficiently reduces the bitrate of digital audio signals by encoding the difference between consecutive samples. This means that instead of transmitting or storing each sample individually, DPCM only transmits the changes or variations in the signal, resulting in a lower data rate.
2. Improved compression efficiency: DPCM reducing redundancy in the signal. It can achieve better compression ratios than PCM, by encoding the difference between two consecutive samples.
3. Lower quantization noise: DPCM encodes the differences between two consecutive samples, it’s less sensitive to quantization errors than PCM.
4. Simplicity of implementation: conceptually, DPCM is more simpler than other compression techniques like transform coding (used in JPEG and MP3), making it easier to implement in hardware or software.

### What Is DPCM?

DPCM stands for Differential Pulse Code Modulation. It is a digital signal compression technique that encodes the difference between consecutive samples in a signal or data stream.

### How does DPCM differ from PCM?

In Pulse Code Modulation(PCM), each sampled signal is quantized and then encoded independently. But in DPCM, find the difference between the two consecutive sample and encode, It reduces the redundancy.

### What is the main advantage of using DPCM?

By using DPCM efficiently reduces the bitrate of digital audio signals by encoding the difference between consecutive samples. This means that instead of transmitting or storing each sample individually, DPCM only transmits the changes or variations in the signal, resulting in a lower data rate.

### When is DPCM commonly used?

DPCM is commonly used in telecommunications for voice and video compression, as well as in image and audio compression applications.