GATE Online Coaching Classes

Digital Communications Online Class-4

By Dr.B.Leela Kumari Assistant Professor, Department of Electronics and Communications Engineering University college of Engineering Kakinada Jawaharlal Nehru Technological University Kakinada

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 1 Session -4 Baseband Transmission

• Delta • advantages and Draw Backs • SNR of DM • Adaptive Delta Modulation • Comparisons • Objective Type questions and Illustrative Problems

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 2 Delta Modulation

• By the DM technique an analog signal can be encoded in to bits .hence in one sense a DM is also PCM • IN DM difference signal is encoded into just a single bit ,hence in one sense a DM is also DPCM • A single bit produces just two possibilities that is used to increase or decrease the estimate

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 3 Block diagram of DM

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 4 The DM consists of

 Comparator Sample and Hold circuit Up-Down Counter D/A Converter

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 5  Comparator makes a comparison between the input base band signal m(t) and its quantized approximation

Δ(t) =V(H) =V(L)

 Up-Down counter increments or decrements its count by one at each active edge of the clock waveform  The count direction(incrementing or decrementing ) is determined by the voltage levels t the “count direction command “ input to the counter

 When this binary input which is also transmitted output S0(t) ,is at level V(H),the counter counts up, When it is at level V(L),the counter counts down  The counter serves as accumulator  D/ Converter: The digital output of the converter is converted to the analog quantized approximation by the D/ Converter

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 6 Response of a Delta Modulator

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 7 Operation

Assume active clock edge is the falling edge

For t< t1 , so that S0(t)=V(H) At t=t1,when the active clock edge appears , the counter is incremented and immediately the signal Jumps up by an mount equal to the step size S

At t=t2 still so S0(t)=V(H) And there is another upward jump in

At t=t3 so S0(t)=V(L) The counter decrements and there is consequent downward jump in by n mount S and so on.

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 8 Delta Modulator Transmitter and Receiver

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 9 6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 10 6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 11 6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 12 • The input given to the decoder is processed and that output is summed up with the output of the predictor, to obtain a better output.

mq(n)=eq (n)+mˆ(n-1)

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 13 Advantages of Delta Modulation

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 14 Draw Backs of Delta Modulation

Hunting Effect Slope overload Error Granular Error

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 15 Hunting Effect

At start up there my be a brief interval when my be a poor approximation To the base band signal m(t) Hence an initial large discrepancy Further even when has caught up to m(t),and even m(t) remains unvarying Hunts swinging up or down ,above and below m(t)

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 16 Slope overload Error The recovered waveform will be distorted when the slope of m(t) is greeter than

the slope of and the DM system is said to be have Slope overload distorted

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 17 Slope overload can be avoided if

S/Ts > |dm(t)/dt|max

If the base band signal is a sinusoidal signal of amplitude A and frequency f, m(t)= A Cos 2πft S/Ts > |dm(t)/dt|max S/Ts > 2πfA To decrease the slope overload error ,increase the step size

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 18 Granular Error

If the variations in m(t) are such that they are with in the step size ,then the is like square wave. This will be recovered as DC, but original signal m(t) is not DC. The noise due to this reason is known as Granular noise Granular noise comes because chosen value of step size is greeter than optimum step size. To reduce the slope overload error , step size needs to be decreased

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 19 Noise in Delta Modulation system

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 20

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 22 6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 23 3 • (SNR)DM = (3/80)(fb/fM) • The actual value of SNR is greater than the value given above • It is found that the value of SNR is 3 (SNR)DM = (3/64)(fb/fM)

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 24 Comparison between PCM and DM

• DM needs Simple circuit • Maximum possible error is ‘S’ in DM as S/2 in PCM. • Hence low SNR • For voice transmission the is 56kbps in PCM where as in DM for the same quality the bit rate is much higher • For good quality transmission , the band width needed by DM is more than PCM

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 25 DM can be recommended for following situations

When band width conservation is desirable When the simple circuitry is of utmost importance

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 26 Adaptive Delta Modulation

• DM are applicable for signals which are having constant slope. • If the slope of the signal is varying continuously, the step size needs to be changed , which is the basic principle of operation of ADM. • ADM is a modification of DM, in which the step size is not kept fixed

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 27 Adaptive Delta Modulation

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 28 The ADM consists of

 Comparator Sample and Hold circuit Digital Processor D/A Converter

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 29 • Digital Processor: it has an accumulator and at each active edge of the clock wave form , generates step S which augments or diminishes the accumulator.

• The step S is not of fixed size but it is always a

multiple of basic step S0

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 30 Response of a Adaptive Delta Modulator

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 31 Generation of S:  The K th active clock edge generates step equal in magnitude to the step generated in response to the (k-1)st clock edge.  This step is added to or subtracted from the accumulator, as required to move toward m(t)  If the direction of the step k is same as at edge (k-1) , then the processor increases the magnitude of the step by an amount S0  If the directions re opposite then the processor decreases the magnitude of the step by an amount S0  S the algorithm is carried out there are clock edges when the total step S=0. In this case at the next clock edge the step is S0 in the direction gin to move toward m(t)  The out put S0(t) is called e(k) which represents the error e(k) = +1 if immediately before the kth edge -1 if immediately before the kth edge at sampling time k, the step size S(k) is to be given by

S(k) = |S(k-1)| e(k)+ S0 e(k-1)

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 32 • as long as the condition persists, the jump in becomes progressively larger, so that the estimate catches up with m(t) sooner than would be the case LDM • For large slope in m(t), develops large jumps. • The ADM system reduces Slope overload error but the quantization error is increased. • The ADM can operate at bit rates of 32kbps with performance comparable to that obtained when using PCM t 64kbps

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 33 Receiver of Adaptive Delta Modulator

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 34 6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 35 Comparisons

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 36 6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 37 Objective Type questions

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 38 1. In Delta modulation, a. One bit per sample is transmitted b. All the coded bits used for sampling are transmitted c. The step size is fixed d. Both a and c are correct

2. In digital transmission, the modulation technique that requires minimum bandwidth is a. Delta modulation b. PCM c. DPCM d. PAM

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 39 3. In Delta Modulation, the bit rate is a. N times the sampling frequency b. N times the modulating frequency c. N times the nyquist criteria d. None of the above

4. The factors that cause error in delta modulation are a. Slope overload distortion b. Granular noise c. White noise d. Both a and b are correct

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 40 5. In delta modulation, the slope overload distortion can be reduced by a. decreasing the step size b. decreasing the granular noise c.decreasing the sampling noise d. increasing the step size

6. In the output of a DM speech encoder, the consecutive pulses are of opposite polarity during time interval 1 ≤ ≤ 2. This indicates that during this interval a . the input to the modulator is essentially constant b. he modulator is going through slope overload c. The accumulator is in saturation d. the speech signal is being sampled at the

Explanation: Given

During the interval ≤ ≤ The consecutive pulses of encoder are of opposite polarity. In between the two adjacent sample values, if the baseband signal changes by an amount less than the step size, the output of Delta Modulator is a sequence of alternate positive and negative pulses. This small change in base band signal indicates that the baseband is almost constant

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 41 7. The modulation techniques used to convert analog signal into digital signal are a. Pulse code modulation b. Delta modulation c. Adaptive delta modulation d. All of the above

8. In Adaptive Delta Modulation, the slope error reduces and a. Quantization error decreases b. Quantization error increases c. Quantization error remains same d. None of the above

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 42 9. The digital modulation scheme in which the step size is not fixed is a. Delta modulation b. Adaptive delta modulation c. DPCM d. PCM

10 Because of variable step size in Adaptive delta modulation a. The dynamic range of the signal is constant b. The dynamic range of the signal is small c. The dynamic range of the signal is Wide d. None of the above

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 43 11. Granular noise occurs when a. Step size is too small b. Step size is too large c. There is interference from the adjacent channel d. Bandwidth is too large

12. Granular noise can be avoided when a. Reducing Step size b. Increasing step size c. both a and b d. None of the above

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 44 13. The crest factor of a waveform is given as – a. 2Peak value/ rms value b. rms value / Peak value c. Peak value/ rms value d. Peak value/ 2rms value

14. The digital modulation technique in which the step size is varied according to the variation in the slope of the input is called a. Delta modulation b. PCM c. Adaptive delta modulation d. PAM

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 45 15. The minimum required amplitude to reduce slope overload distortion for a sinusoidal modulating signal of frequency f ( S-step size) a. Sfs/2 b. STs/2 c. Sfs/2πf d. Sfs/2π

16. Linear Delta Modulation suitable for a. Signals having constant slope b. Signals having varying slope c. Both a and b d. None of the above

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 46 17. The input to the DM system is m(t) =5cos2π1000t. The pulse rate is 56,000 pulse/sec. Determine the step size.

Sol : Step size =2πfmAm/fs = 2πfmAm/(1/Ts)

Am = 5v

1/Ts = 56000 Δ = (5×2π×1000)/56000

Δ =0.56v 18. Input to the DM is m(t)=Am cos 2π fmt. Step size is 0.628v sampling rate is 40,000 samples/sec. The combination of sinusoidal signal amplitude and frequency for which the slope overload distortion occurs is

Sol : Δ /TS < |d/dt m(t)|max

Δ =0.628 m(t)=Amcos2π fmt

Ts = 1/ 40,000 dm(t)/dt =2π Am fm Sin 2π fm t

|dm(t)/dt|max= 2π fmAm

0.628× 40000< 2πfmAm

Amfm> 0.628× 40000/2π

Amfm> 40k. 19. The input to a linear delta modulator having a step-size ∆= 0.628 is a sine wave with

frequency fm and peak amplitude Em. If the sampling frequency fs = 40 KHz, the combination of the sine-wave frequency and the peak amplitude, where slope overload will take place is

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 49 20. The minimum step-size required for a Delta-Modulation operating at 32K samples/sec to track the signal (here u(t) is the unit-step function)

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 50 21. The minimum sampling frequency (fs)min required to avoid slope overload when x(t) = cos(2π800t) and δ = 0.1 is (a) 23.12 kHz (b) 50.25 kHz (c) 98.12 kHz (d) 75.67 kHz

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 51 22. Let a message signal m(t) be the input to a delta modulator where m (t) = 6 2 sin ( 2π × 103 ) +4 [Sin(4 π 103 ) t] v with t in seconds . The minimum pulse rate that will prevent slope overload is (given that the step size is 0.314 V) (a) 280 × 103/s (b) 380 × 103/s (c) 480 × 103/s (d) 180 × 103/s

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 52 23.A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size ∆ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is

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6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 54 6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 55 26.

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 56 6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 57 27.

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 58 6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 59 Minimum Transmission Bandwidth = nfm = 1x32k 32 KHz

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 60 28.

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6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 62 30.

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 63 References 1. communication systems by B.P.Lathi 2. Principles of communication systems by Herber Taub.Donald & Schilling,Goutam Saha 3. Digital Communications ,Design for real World by Andy Bateman 4. Digital Communications by Dr.K.N.Hari Bhat ans Dr.D.Ganesh Rao 5. Communication Syatems,by R.P.Singh , S D Sapre 6. Digital Communications second edition by CH. Kranthi Rekha 7. Digital Communications theory ,techniques and applications by R.N.Mutagi 8. Digital Communications by P.Rama Krishna Rao 9. coding Techniques by R. Avudaiammal 9. Wiley Acing the GATE Examination For Electronics and Communication Engineering 10. https://www.aceenggacademy.com/ 11. gate study.com 12. https://www.madeeasy.in/

Disclaimer: The material presented in this presentation is taken from various standard Textbooks and Internet Resources and the presenter is acknowledging all the authors.

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 64 Thank You

6/24/2020 Dr. B. Leela Kumari UCEK JNTUK Kakinada 65