Differential Pulse Code Modulation (DPCM) is a technique for converting analog signals to digital by sampling the analog signal and quantizing the difference between the current and predicted values. DPCM reduces bandwidth and quantization error compared to traditional Pulse Code Modulation (PCM) by exploiting the correlation between successive samples, making it efficient for applications like audio compression. The document discusses DPCM's advantages, coding methods, and practical uses, including its relationship with Adaptive Differential Pulse Code Modulation (ADPCM).

1. DIFFERENTIAL PULSE CODE MODULATION
SUBMITTED BY
***SURYA TEJA S – 150040841
NAVEEN T – 150040849
TARUN NAGA SAI TEJA K - 150040859
SAI SEERESHA T – 150040872

2. INTRODUCTION

3. PULSE CODE MODULATION:
PULSE CODE MODULATION IS A METHOD THAT IS USED TO CONVERT AN
ANALOG SIGNAL INTO A DIGITAL SIGNAL, SO THAT MODIFIED ANALOG
SIGNAL CAN BE TRANSMITTED THROUGH THE DIGITAL
COMMUNICATION NETWORK.
THE PULSE CODE MODULATION PROCESS INCLUDES THREE STEPS:
SAMPLING, QUANTIZATION, AND ENCODING.
THE QUANTIZING AND ENCODING ARE PERFORMED IN SAME CIRCUIT
CALLED ANALOG TO DIGITAL CONVERTER

6. • SAMPLING
• IN SIGNAL PROCESSING, SAMPLING IS THE REDUCTION OF
A CONTINUOUS-TIME SIGNAL TO A DISCRETE-TIME SIGNAL. A COMMON
EXAMPLE IS THE CONVERSION OF A SOUND WAVE (A CONTINUOUS
SIGNAL) TO A SEQUENCE OF SAMPLES (A DISCRETE-TIME SIGNAL).
• A SAMPLE IS A VALUE OR SET OF VALUES AT A POINT IN TIME AND/OR
SPACE.
• A SAMPLER IS A SUBSYSTEM OR OPERATION THAT EXTRACTS SAMPLES
FROM A CONTINUOUS SIGNAL.
• A THEORETICAL IDEAL SAMPLER PRODUCES SAMPLES EQUIVALENT TO
THE INSTANTANEOUS VALUE OF THE CONTINUOUS SIGNAL AT THE
DESIRED POINTS.

8.  QUANTIZATION: THE PROCESS OF CONVERTING THE ORIGINAL SIGNAL M (T) INTO A NEW
SIGNAL (OR) QUANTIZED SIGNAL MQ (T) WHICH IS AN APPROXIMATION OF M (T) IS
KNOWN AS QUANTIZATION.
 THE MINIMUM TRANSMISSION BANDWIDTH IN PCM IS GIVEN AS,
BW= N*FM
HERE N IS THE NUMBER OF BITS USED TO REPRESENT ONE PULSE. FM IS THE MAXIMUM
SIGNAL FREQUENCY.
 TO GET A PULSE CODE MODULATED WAVEFORM FROM AN ANALOG WAVEFORM AT THE
TRANSMITTER END (SOURCE) OF A COMMUNICATIONS CIRCUIT, THE AMPLITUDE OF THE
ANALOG SIGNAL SAMPLES AT REGULAR TIME INTERVALS. THE SAMPLING RATE OR
NUMBER OF SAMPLES PER SECOND IS SEVERAL TIMES THE MAXIMUM FREQUENCY. THE
MESSAGE SIGNAL CONVERTED INTO BINARY FORM WILL BE USUALLY IN THE NUMBER OF
LEVELS WHICH IS ALWAYS TO A POWER OF 2. THIS PROCESS IS CALLED QUANTIZATION.

10. WHY WE ARE GOING FOR DPCM?
• TO IMPROVE THE ENCODING EFFICIENCY OF ANALOG TO DIGITAL CONVERSION.
• INSTEAD OF TRANSMITTING THE SAMPLE VALUES, WE TRANSMIT THE DIFFERENCE BETWEEN THE SUCCESSIVE
SAMPLE VALUES.
• M(K) IS KTH SAMPLE, INSTEAD OF TRANSMITTING M(K)
• D(K) = DQ(K) -M(K -1)
• AT THE RECEIVER, KNOWING PRECIOUS SAMPLE VALUE M(K-1) , THE M(K) IS RECONSTRUCTED.
• DIFFERENCE BETWEEN THE SUCCESSIVE SAMPLES IS GENERALLY MUCH SMALLER THAN SAMPLE VALUES. ’ P M ’ IS
REDUCED CONSIDERABLY.
ΔV = / P M L
• PREDICTING THE VALUES OF KTH SAMPLE M(K) FROM PREVIOUS SAMPLE M(K) FROM M(K) CAN BE ESTIMATED, THEN
D(K) =M(K) -M(K) AT THE RECEIVER M(K) FROM PREVIOUS SAMPLE AND GENERATE M(K) BY ADDING D(K) TO
ESTIMATE M(K)

11. DIFFERENTIAL PULSE CODE MODULATION:
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. IT THEN ENCODES THE SIGNAL TO
FORM A DIGITAL VALUE.
BASIC CONCEPT OF DPCM - CODING A DIFFERENCE, IS BASED ON THE FACT
THAT MOST SOURCE SIGNALS SHOW SIGNIFICANT CORRELATION
BETWEEN SUCCESSIVE SAMPLES SO ENCODING USES REDUNDANCY IN
SAMPLE VALUES WHICH IMPLIES LOWER BIT RATE.

13. ADVANTAGES OF DPCM:
1)BANDWIDTH REQUIREMENT OF DPCM IS LESS COMPARED TO PCM.
2) QUANTIZATION ERROR IS REDUCED BECAUSE OF PREDICTION FILTER.
3) NUMBERS OF BITS USED TO REPRESENT .ONE SAMPLE VALUE ARE ALSO
REDUCED COMPARED TO PCM.

14. AN ILLUSTRATION OF DPCM'S ADVANTAGES
OVER PCM
• A TYPICAL EXAMPLE OF A SIGNAL GOOD FOR DPCM IS A LINE IN A CONTINUOUS-
TONE (PHOTOGRAPHIC) IMAGE.
• FOR ILLUSTRATION, WE PRESENT TWO HISTOGRAMS MADE FROM THE SAME PICTURE
WHICH WERE CODED IN TWO WAYS. THE HISTOGRAMS SHOW THE PCM AND
DPCM SAMPLE FREQUENCIES, RESPECTIVELY.
• ON THE FIRST HISTOGRAM, LARGE NUMBER OF SAMPLES HAS A SIGNIFICANT
FREQUENCY AND WE CANNOT PICK ONLY A FEW OF THEM WHICH WOULD BE
ASSIGNED SHORTER CODE WORDS TO ACHIEVE COMPRESSION. ON THE SECOND
HISTOGRAM PRACTICALLY ALL THE SAMPLES ARE BETWEEN -20 AND +20, SO WE
CAN ASSIGN SHORT CODE WORDS TO THEM AND ACHIEVE A SOLID COMPRESSION
RATE.

17. • DPCM ENCODING AND DECODING
• A SIMPLE CASE OF DPCM QUANTIZES THE DIFFERENCE
BETWEEN THE SIGNAL'S CURRENT VALUE AND ITS VALUE AT
THE PREVIOUS STEP.
• THUS THE PREDICTOR IS JUST Y(K) = X (K - 1).
• THE CODE BELOW IMPLEMENTS THIS SCHEME. IT ENCODES
A SAWTOOTH SIGNAL, DECODES IT, AND PLOTS BOTH THE
ORIGINAL AND DECODED SIGNALS. THE SOLID LINE IS THE
ORIGINAL SIGNAL, WHILE THE DASHED LINE IS THE
RECOVERED SIGNALS. THE EXAMPLE ALSO COMPUTES THE
MEAN SQUARE ERROR BETWEEN THE ORIGINAL AND
DECODED SIGNALS.

18. MATLAB CODE
• PREDICTOR = [0 1]; % Y(K)=X(K-1)
• PARTITION = [-1:.1:.9];
• CODEBOOK = [-1:.1:1];
• T = [0:PI/50:2*PI];
• X = SAWTOOTH(3*T); % ORIGINAL SIGNAL
• % QUANTIZE X USING DPCM.
• ENCODEDX = DPCMENCO(X,CODEBOOK,PARTITION,PREDICTOR);
• % TRY TO RECOVER X FROM THE MODULATED SIGNAL.
• DECODEDX = DPCMDECO(ENCODEDX,CODEBOOK,PREDICTOR);
• PLOT(T,X,T,DECODEDX,'--')
• DISTOR = SUM((X-DECODEDX).^2)/LENGTH(X) % MEAN SQUARE ERROR

19. ADVANTAGES
• DIGITAL COMMUNICATION TECHNIQUES HAVE PROVED THEIR PREFERENCE OVER
ANALOG COMMUNICATION TECHNIQUES DUE TO THEIR HIGHER RELIABILITY,
FLEXIBILITY AND COMPATIBILITY. HOWEVER, THE COMMONLY USED DIGITAL
COMMUNICATION TECHNIQUES SUCH AS PCM (PULSE CODED MODULATION) AND
LDM (LINEAR DELTA MODULATION) CAUSE QUANTIZATION ERROR, SLOPE OVERLOAD
DISTORTION, AND GRANULAR NOISE WHICH ALL NEGATIVELY AFFECT THE
COMMUNICATION PROCESS. IN ORDER TO SOLVE THE AFOREMENTIONED PROBLEMS,
ADM (ADAPTIVE DELTA MODULATION) AND DPCM (DIFFERENTIAL PULSE CODED
MODULATION) ARE DISCUSSED AND IMPLEMENTED. DPCM SYSTEM SOLVES THE
QUANTIZATION ERROR PROBLEM, AND ADM SOLVES THE SLOPE OVERLOAD
DISTORTION AND THE GRANULAR NOISE PROBLEMS.

20. • DPCM - PRACTICAL USES
• IN PRACTICE, DPCM IS USUALLY USED WITH COMPRESSION TECHNIQUES, LIKE
COARSER QUANTIZATION OF DIFFERENCES CAN BE USED, WHICH LEADS TO
SHORTER CODE WORDS. THIS IS USED IN ADAPTIVE DPCM (ADPCM), A
COMMON AUDIO COMPRESSION METHOD. ADPCM CAN BE WATCHED AS A
SUPERSET OF DPCM.
IN ADPCM QUANTIZATION STEP SIZE ADAPTS TO THE CURRENT RATE OF
CHANGE IN THE WAVEFORM WHICH IS BEING COMPRESSED.
DIFFERENT ADPCM IMPLEMENTATIONS HAVE BEEN STUDIED. THE MORE
POPULAR IS IMA ADPCM, THIS ADPCM IMPLEMENTATION IS BASED ON THE
ALGORITHM PROPOSED BY INTERACTIVE MULTIMEDIA ASSOCIATION. IMA
ADPCM STANDARD SPECIFIES COMPRESSION OF PCM FROM 16 DOWN TO 4
BITS PER SAMPLE.
THE GOOD SIDE OF THE ADPCM METHOD IS MINIMAL CPU LOAD, BUT IT HAS
SIGNIFICANT QUANTIZATION NOISE AND ONLY MEDIOCORE COMPRESSION
RATES CAN BE ACHIEVED(4:1).

21. MERITS OF DPCM:
BANDWIDTH REQUIREMENT OF DPCM IS LESS COMPARED TO PCM.
QUANTIZATION ERROR IS REDUCED BECAUSE OF PREDICTION FILTER
NUMBERS .OF BITS USED TO REPRESENT .ONE SAMPLE .VALUE ARE
ALSO REDUCED
COMPARED TO PCM.

22. REAL LIFE APPLICATIONS