 Hello everyone. Welcome to this session. I am Deepali Vadkar working as assistant professor at WIT Solapur. In this video session, we will see differential pulse code modulation system, DPCM system. At the end of this video lecture, student will be able to describe working of DPCM transmitter and receiver. Student will be able to state advantages, disadvantages and applications of DPCM. These are the contents. Before starting DPCM system, pause the video and recall what is PCM. PCM that is pulse code modulation, it is digital representation of analog signal that takes samples of amplitude of analog signals at regular interval. This sampled analog signal is get converted into the binary data. Before starting to the DPCM system, let us see the demerits of this PCM system. Suppose there is one analog signal, continuous time signal X of t. This continuous time signal here represented by this dotted lines. This continuous time signal sampled here at sampling rate FS. So, here sampling period is TS. We can observe at samples four TS, five TS and six TS. These three samples are encoded at the same value that is 110. Now these samples can be carried by single sample. Here same information is present but this same information is carried by three different samples and it is three different code. Its meaning is that there is redundant data. If the redundancy is reduced then the bit rate also reduces and number of bits required to transmit that information that number of bits also reduces. So, this redundancy can be reduced by using one another technique that is the DPCM or differential pulse code modulation. DPCM it is the technique of analog to digital signal conversion. DPCM works on the principle of prediction. The present sample is predicted here by using the value of past sample. This prediction may not be exact but it is nearly close to the value of that sample. Now the basic steps in this DPCM that is first the analog signal is sampled then the difference between sampled signal and predicted value of signal that difference is quantized and then that quantized signal is get encoded. Let us see the DPCM transmitter. Here the input signal it is nothing but X of NTS. This X of NTS it is the sampled version of this X of T that is the continuous time signal. Now another signal input to this comparator that signal is a X dash of NTS. This X dash of NTS it is nothing but predicted signal. This predicted signal is produced from this prediction filter. Now comparator compares this sampled input and this predicted signal and it gives the result that is the error signal. This error signal is represented by E of NTS. This error is known as prediction error. This error signal or prediction error is defined as E of NTS is equal to X of NTS minus X dash of NTS. Prediction error is given input to the quantizer. At the output of quantizer we get a quantized error signal. This is represented by Eq of NTS. So Eq of NTS or quantized error signal can be defined as it is combination of error signal E of NTS and Q of NTS which is nothing but quantization error signal. Now this error signal is given to the encoder. Encoder encodes this signal quantized signal and at the output of this encoder we get the DPCM signal which is nothing but one binary data. Quantized error signal again given to the adder which is present here. Another input to this adder that is nothing but X Q of NTS. So output of this adder this is given to the prediction filter which is represented by X Q of NTS. This is nothing but input to the prediction filter. So the prediction filter input here X Q of NTS we can write it is Eq of NTS plus X dash of NTS. Put value of Eq of NTS that is the quantized signal into this equation. Then that equation becomes X Q of NTS is equal to E of NTS plus Q of NTS plus X dash of NTS but the E of NTS is equal to X of NTS minus X dash of NTS. Now same signal we can write E of NTS plus X dash of NTS which is equal to X of NTS. Now in this equation put this E of NTS plus X dash of NTS it is equal to X of NTS. Then this equation becomes X Q of NTS is equal to X of NTS plus Q of NTS. Now from this equation we can say that this quantized version of this signal is depends upon the input sample signal and this quantization error signal. But it doesn't depend upon the any characteristic of this prediction filter. Let us see one example. Suppose the input sample signal its amplitude is 1.1 so value of X of NTS is 1.1 this 1.1 is given to the adder then the initially the prediction filter output consider that prediction filter output is 0. Now this comparator compares both this signal so 1.1 minus 0 its error signal it is nothing but 1.1 okay. Now this error signal is quantized at the standard level okay so its nearest standard level is 1. After that this signal is encoded into 001. Now for this step the DPCM output is 001 okay. Now X Q of NTS that is the input to the prediction at this step this input is 0 plus 1 that is nothing but 1. After that if we give the input sample 1.2 then here the previous predicted value is 1 then the difference between 1.2 and 1 this is nothing but 0.2 and this signal is quantized at the nearest standard value that is the 0. So at this step X Q of NTS it becomes 1 plus 0 that is 1. In this way here this AQ of NTS for this respective sample this data bit is nothing but 10010 okay. Now this data bit is encoded by using this encoder so the transmitted data that is nothing but 001, 000, 000, 001 and so on okay. Let us see the working at DPCM receiver that is DPCM demodulator. Here this is the input data to the decoder decoder converts this input data into the quantized error signal then here the adder is present the another input to this adder that is the predicted value from this predictor filter then the output of this adder it is nothing but X Q of NTS which is equal to X dash of NTS plus X Q of NTS okay and this output given to the low pass filter low pass filter converts this staircase signal into the continuous time signal. Now let us see the same example how these samples are recovered again here. Suppose the input bit is 001 then it is given to the decoder then at that time this 001 is get converted into the quantized level that is 1 after that the predictor output initially predictor output is 0 okay. So consider this predictor output is 0 here adder add these two signals and its output is 0 plus 1 that is 1 okay. Now this 1 is given input to the low pass filter low pass filter input here 1 is represented by that staircase approximate signal and the output of low pass filter it is nothing but continuous time signal for that time period okay. Now this same 1 input is given to the predictor okay in this way the recovered signals or recovered samples that is nothing but X Q of NTS here okay. So recovered samples here that is 1 1 1 2 and 2 so and so on. So these recovered samples represented by staircase signal when we give the input to the low pass filter this staircase signal then low pass filter converts this signal into the continuous time signal okay. So at the output of low pass filter the original data or original signal is recovered. The applications of DPCM this technique mainly used for a speech image and audio signal compression. This method is suitable for real-time applications. Next is advantages of DPCM the bandwidth required for DPCM is less as compared to PCM quantization error is reduced because of prediction filter and number of bits used to represent one sample value are also reduced compared to PCM. These are the references thank you.