DIFFERENTIAL PULSE CODE MODULATION

SUBMITTED BY

***SURYA TEJA S – 150040841

NAVEEN T – 150040849

TARUN NAGA SAI TEJA K - 150040859

SAI SEERESHA T – 150040872

INTRODUCTION

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

• 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.

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.

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)

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.

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.

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.

• 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.

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

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.

• 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).

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.

REAL LIFE APPLICATIONS