# Differential Pulse Code Modulation Working and Application

Differential pulse code modulation is a technique of analog to digital signal conversion. This technique samples the analog signal and then quantizes the difference between the sampled value and its predicted value, then encodes the signal to form a digital value. Before going to discuss differential pulse code modulation, we have to know the demerits of PCM (Pulse Code Modulation). The samples of a signal are highly correlated with each other. The signal’s value from the present sample to the next sample does not differ by a large amount. The adjacent samples of the signal carry the same information with a small difference. When these samples are encoded by the standard PCM system, the resulting encoded signal contains some redundant information bits. The below figure illustrates this.

The above figure shows a continuing time signal x(t) denoted by a dotted line. This signal is sampled by flat-top sampling at intervals Ts, 2Ts, 3Ts…nTs. The sampling frequency is selected to be higher than the Nyquist rate. These samples are encoded by using 3-bit (7 levels) PCM. The samples are quantized to the nearest digital level as shown by small circles in the above figure. The encoded binary value of each sample is written on the top of the samples. Just observe the above figure at samples taken at 4Ts, 5Ts, and 6Ts are encoded to the 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 let consider the samples at 9Ts and 10Ts, the difference between these samples only due to the last bit and first two bits are redundant since they do not change. So in order to make the process this redundant information and to have a better output. It is an intelligent decision to take a predicted sampled value, assumed from its previous output and summarise them with the quantized values. Such a process is called a Differential PCM (DPCM) technique.

## Principle of Differential Pulse Code Modulation

If the redundancy is reduced, then the overall bitrate will decrease and the number of bits required to transmit one sample will also reduce. This type of digital pulse modulation technique is called differential pulse code modulation. The DPCM works on the principle of prediction. The value of the present sample is predicted from the previous samples. The prediction may not be exact, but it is very close to the actual sample value.

**Differential Pulse Code Modulation **Transmitter

The below figure shows the DPCM transmitter. The transmitter consists of a comparator, quantizer, prediction filter, and an encoder.

The sampled signal is denoted by x(nTs) and the predicted signal is indicated by x^(nTs). The comparator finds out the difference between the actual sample value x(nTs) and the predicted value x^(nTs). This is called signal error and it is denoted as e(nTs)

e(nTs)= x(nTs)- x^( nTs) …….(1)

Here the predicted value x^(nTs) is produced by using a prediction filter(signal processing filter). The quantizer output signal eq(nTs) and the previous prediction is added and given as input to the prediction filter, this signal is denoted by xq(nTs). This makes the prediction closer to the actually sampled signal. The quantized error signal eq(nTs) is very small and can be encoded by using a small number of bits. Thus the number of bits per sample is reduced in DPCM.

The quantizer output would be written as,

eq(nTs)= e(nTs)+ q(nTs) ……(2)

Here q(nTs) is quantization error. From the above block diagram the prediction filter input xq(nTs) is obtained by sum of x^(nTs) and the quantizer output eq(nTs).

i.e, xq(nTs) = x^(nTs)+ eq(nTs).………. (3)

by substituting the value of eq(nTs) from the equation (2) in equation (3) we get,

xq(nTs) = x^(nTs)+ e(nTs)+ q(nTs)……. (4)

Equation (1) can written as,

e(nTs)+ x^( nTs) = x(nTs)……. (5)

from the above equations 4 and 5 we get,

xq(nTs) = x(nTs)+ x(nTs)

Therefore, the quantized version of signal xq(nTs) is the sum of original sample value and quantized error q(nTs). The quantized error can be positive or negative. So the output of the prediction filter does not depend on its characteristics.

**Differential Pulse Code Modulation **Receiver

In order to reconstruct the received digital signal, the DPCM receiver (shown in the below figure) consists of a decoder and prediction filter. In the absenteeism of noise, the encoded receiver input will be the same as the encoded transmitter output.

As we discussed above, the predictor undertakes a value, based on the previous outputs. The input given to the decoder is processed and that output is summed up with the output of the predictor, to obtain better output. That means here first of all the decoder will reconstruct the quantized form of the original signal. Therefore the signal at the receiver differs from the actual signal by quantization error q(nTs), which is introduced permanently in the reconstructed signal.

S. NO | Parameters | Pulse Code Modulation (PCM) | Differential Pulse Code Modulation (DPCM) |

1 | Number of bits | It uses 4, 8, or 16 bits per sample | < PCM bits |

2 | Levels, step size | Fixed step size. Cannot varied | A fixed number of levels are used. |

3 | Bit redundancy | Present | Can permanently remove |

4 | Quantization error and distortion | Depends on the number of levels used | Slope overload distortion and quantization noise are present but very less as compared to PCM |

5 | The bandwidth of the transmission channel | Higher bandwidth has been required since the number of bits is absent | Lower than PCM bandwidth |

6 | Feedback | No feedback in Tx and Rx | Feedback exists |

7 | Complexity of notation | Complex | Simple |

8 | Signal to noise ratio (SNR) | Good | Fair |

### Applications of DPCM

The DPCM technique mainly used Speech, image and audio signal compression. The DPCM conducted on signals with the correlation between successive samples leads to good compression ratios. In images, there is a correlation between the neighboring pixels, in video signals, the correlation is between the same pixels in consecutive frames and inside frames (which is the same as correlation inside the image).

This method is suitable for real-Time applications. To understand the efficiency of this method of medical compression and real-time application of medical imaging such as telemedicine and online diagnosis. Therefore, it can be efficient for lossless compression and implementation for lossless or near-lossless medical image compression.

This is all about Differential Pulse Code Modulation working. We consider that the information given in this article is helpful for you to a better understanding of this concept. Furthermore, any queries regarding this article or any help in implementing electrical and electronics projects, you can approach us by commenting in the comment section below. Here is a question for you, What is the role of the predictor in the DPCM technique?

I highly appriciate this article. It has helped me undersndand dpcm

Hi Bonface Achieng

Thank you for taking the time to review your stay with us

Band width for pcm and dpcm is same right

Hi Hema

The DPCM need less bandwidth as compared to PCM

It is observed that if the sampling takes place at a rate which is higher than the Nyquist rate, then there is a correlation between successive samples of the signal x (t). Hence we can predict the range of next required increment or decrement in x(t) at the predictor output, if we know the past sample value or the difference. This reduces the difference or error between x (to and X (t Therefore to encode this small value of error the DPCM system requires less number of bits which will ultimately reduce the bit rate. This is the role predictor in DPCM system.