rr310405 digital communications

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Code No: RR310405 Set No. 1

III B.Tech I Semester Supplementary Examinations, February 2007DIGITAL COMMUNICATIONS

( Common to Electronics & Communication Engineering and Electronics &Telematics)

Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks⋆ ⋆ ⋆ ⋆ ⋆

1. (a) Explain the different types of Sampling. [10]

(b) Obtain the Nyquist rate and Nyquist interval for the signal 10 Cos (2000πt)Cos ( 4000πt) based on

i. low pass sampling theory, and

ii. band pass sampling theory. [6]

2. Four signals Cos ω0t, 0.2 Cos ω0t, 2 Cos 2 ω0t and Cos 4 ω0t are to be multi-plexed in a TDM system. Find the minimum sampling rate f s , minimum intervaland the associated commutator speed. If the commutator rotates at f s/4, and f s/8revolutions per sec., determine the number of o/p samples of each signal per ro-tation. Illustrate and explain this process with neat schematics for a commutatorswitch rotating at a speed of f s/4 revolutions per sec., showing the transmittingand receiving sides. Discuss the necessity of synchronization for this case. [16]

3. (a) Why the overall transfer function of the duo-binary filter is called as Half-cyclecosine function. [8]

(b) Give the Impulse response of the duo-binary filter and sketch the amplitudeand phase response. [8]

4. (a) Explain how eye patterns are used for monitoring the performance of baseband PAM system. [8]

(b) What is the necessity of shaping transmitted signal spectrum. [8]

5. (a) Prove that the mean value of the quantization error is inversely proportionalto the square of the number of quantization levels.

(b) What is the function of a predictor in a DPCM system. [10+6]

6. (a) Explain the working of delta modulation system with neat block diagram.(b) Clearly bring out the difference between granular noise and slope over load

error. [8+8]

7. (a) Derive an expression for probability of bit-error for a binary non-coherent FSKdemodulator.

(b) Binary data is transmitted over a telephone line with usable bandwidth of 2400 Hz using the FSK signaling scheme. The transmit frequencies are 2025& 2225 Hz, and the data rate is 300 bits/Sec. The average signal to noise

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power ratio at the output of the channel is 6dB. Calculate Pe for the coherentand non coherent demodulation schemes. [8+8]

8. (a) Explain encoding operation in linear block codes. [8]

(b) Find the output code word for the following convolutional encoder for a mes-

sage sequence 10011. {As shown in the Figure1} [8]

Figure 1:

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1. (a) Distinguish between natural sampling and flat top sampling with neat schemat-ics, listing out their merits and demerits. [8]

(b) A signal m(t) = 4 Cos (60 πt) + 2 Cos (160 πt) + Cos (280 πt) is sampled at

i. 150 Hz,

ii. 75 Hz,

iii. 300 Hz.Find the frequency components of the signal that appear at the output of anideal LPF with cut off at 290 Hz., in each case. What is the Nyquist rate of sampling and Nyquist interval for m(t)? [8]

2. (a) Explain the principles of TDM. List out their merits, demerits and applica-tions. [8]

(b) Explain the method of generation and detection of PAM signals with neatschematics. [8]

3. (a) What are the two key functional operations involved in correlative coding? [8]

(b) i. For the data stream 0010110, find the duo-binary decoded wave formand give the electrical representation of the data obtained at stages of decoding. [4]

ii. Verify that Duo-binary decoding results in bandwidth reduction duringtransmission by assuming the message sequence to be transmitted is analternative 1/0 sequence. [4]

4. (a) What is meant by Synchronization in the base band PAM. What are thedifferent methods to obtain Synchronization? [8]

(b) The T1 carrier system used in digital telephony multiplexes 24 voice channels

based on 8-bit PCM. Each voice signal is usually put through a lowpass filterwith cutoff frequency of about 3.4 KHz. The filtered voice signal is sampledat 8KHz. In addition, a single bit is added at the end of the frame for thepurpose of synchronization. Calculate

i. the duration of each bit

ii. the resultant transmission rate and

iii. the minimum required transmission bandwidth. [8]

5. (a) Draw the block diagram of PCM Generator and explain each block.

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(b) Determine the Transmission Bandwidth in PCM. [8+8]

6. In a single-integration DM system, the voice signal is sampled at a rate of 64kHz.Themaximum signal amplitude is Amax=1.

(a) Determine the minimum value of the step size σ to avoid slope over load error.

(b) Determine the granular noise power if the voice signals bandwidth is 3.5 kHz.

(c) Assuming that the voice signal is sinusoidal, determine output signal powerand SNR

(d) Determine the minimum transmission bandwidth. [4+4+4+4]

7. A statistically independent sequence of equiprobable binary digits is transmittedover a channel having finite band width using the rectangular signaling wave formis taken. The bit rate is rb and the channel noise has a psd Gn(f) given by

Gn(f)=G0[1+(f/f1)2)]−1

(a) find the transfer function of the optimum receiver and calculate the probabilityof error. [8]

(b) If an integrate and dump receiver is used instead of the optimum receiver, findthe probability of error for the optimum receiver. [8]

8. (a) Explain the table lookup decoding in linear block codes using standard array.

[8]

(b) The generator polynomial of a (7,4) cyclic code is g (x)= 1+x+x3. Find thecode vector for the message vector D= (1111) using systematic and nonsys-

tematic form. [8]

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1. (a) With neat diagrams, explain the principle of working a sample and hold circuit.List out its applications. [8]

(b) Show that∞

R=−∞

x(RT s) = f s∞

n=−∞

X (nf s) , where x(t) is a signal band

limited to f 1 , X(f) is the spectrum of x(t), and f s = 1

T s= 2f 1 is the Nyquist

sampling rate. [8]

2. (a) Sketch and explain the typical waveforms of PWM signals, for leading edge,trailing edge and symmetrical cases.

(b) Compare the analog pulse modulation schemes with CW modulation systems.

(c) Show that a PAM signal can be expressed as the convolution of an instanta-neously sampled signal, and a rectangular pulse p(t) of the form

p (t) =

1, |t| ≤ τ /20 elsewhere

[5+5+6]

3. (a) Explain how the residual effect of the channel is responsible for Inter SymbolInterference (ISI). [8]

(b) Explain about three tap preset equalizer. [8]

4. (a) What is meant by Synchronization in the base band PAM. What are thedifferent methods to obtain Synchronization? [8]

(b) The T1 carrier system used in digital telephony multiplexes 24 voice channelsbased on 8-bit PCM. Each voice signal is usually put through a lowpass filterwith cutoff frequency of about 3.4 KHz. The filtered voice signal is sampledat 8KHz. In addition, a single bit is added at the end of the frame for thepurpose of synchronization. Calculate

i. the duration of each bitii. the resultant transmission rate and

iii. the minimum required transmission bandwidth. [8]

5. (a) Prove that the mean value of the quantization error is inversely proportionalto the square of the number of quantization levels.

(b) What is the function of a predictor in a DPCM system. [10+6]

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6. A Delta modulator system is designed to operate at five times the Nyquist rate for asignal with 3 kHz bandwidth. Determine the maximum amplitude of a 2 kHz inputsinusoid for which the delta Modulator does not have slope overload. Quantizationstep size is 250mv .Derive the formula used. [16]

7. (a) With a neat block diagram explain noncoherent detection of ASK receiver,and hence derive the expression for probability of error

Pe ≈ 1/2 exp (-A2/8N0) if A2>>N0 [8]

(b) Binary data has to be transmitted over a telephone link that has a usablebandwidth at 3000Hz, and a maximum achievable signal-to-noise power ratioof 6 dB at its output.

i. Determine the maximum signaling rate and Pe if a coherent ASK schemeis used for transmitting binary data through this channel.

ii. If the data rate is maintained at 300 bits/Sec, calculate the error proba-

bility. [8]

8. (a) Design an encoder for the (7,4) binary cyclic code generated by g(x) = 1+x+x3

and verify its operation using the message vector (0101).

(b) What are the differences between block codes and the convolutional codes?[8+8]

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1. (a) For the signal x(t) =

Sa

t

2

2, estimate –

i. The Nyquist sampling interval and frequency,

ii. Bandwidth.

Describe the effects of sampling at 10 rad./sec., explaining the requirementsof ideal LPF and the resulting signal reconstruction. Take Sa(t) = Sin t

t.

(b) Define the sampling theorem as applicable to voice signals on telephone lines.[16]

2. (a) Sketch and explain the typical waveforms of PWM signals, for leading edge,trailing edge and symmetrical cases.

(b) Compare the analog pulse modulation schemes with CW modulation systems.

(c) Show that a PAM signal can be expressed as the convolution of an instanta-neously sampled signal, and a rectangular pulse p(t) of the form

p (t) =

1, |t| ≤ τ /20 elsewhere

[5+5+6]

3. (a) What is meant by Duo-binary signaling? Give the scheme of Duo-binarysignaling and explain. [8]

(b) A telephone signal with a cutoff frequency of 4 KHz is digitized in to 8 bitsamples at the Nyquist sampling rate fs = 2w. Assuming raised cosine filteringwith a roll-off factor unity.Calculate

i. The transmission bandwidth and

ii. The quantization signal to noise ratio. [8]

4. (a) Explain the necessity of Equalization in base band PAM systems. [8]

(b) Find the duo-binary encoded sequence for the data sequence 011010. How itis detected? [8]

5. A message signal m(t) is transmitted by binary PCM without compression .If theSNR is required to be at least 47dB, determine the minimum value of L required,assuming that m(t) is sinusoidal. Determine the SNR obtained with this minimumL. Derive the formulae used. [16]

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6. A Delta modulator system is designed to operate at five times the Nyquist rate for asignal with 3 kHz bandwidth. Determine the maximum amplitude of a 2 kHz inputsinusoid for which the delta Modulator does not have slope overload. Quantizationstep size is 250mv .Derive the formula used. [16]

7. (a) Write down the modulation waveforms for transmitting binary informationover baseband channels, for the following modulation schemes.

i. ASK

ii. FSK

iii. PSK and

iv. Baseband pulse shaping followed by DSB modulation.

what are the advantages and disadvantages of digital modulation schemes?

(b) Discuss base band transmission of M-ary data. [6+10]

8. The parity check bits of a (8,4) block code are generated by

c5 = d1 + d2 + d4

c6 = d1 + d2 + d3

c7 = d1 + d3 + d4

c8 = d2 + d3 + d4, where d1, d2, d3, and d4 are the message bits.

(a) Find the generator matrix and the parity check matrix for this code.

(b) Find the minimum weight of this code

(c) Find the error detecting capabilities of this code

(d) Show through an example that this code can detect three errors per code word.[16]

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