INFORMATION THEORY AND CODING SUBJECT …librarian/Question Papers/Q-PAPERS 2009/B.TEC... · INFORMATION THEORY AND CODING SUBJECT CODE: EC-509 Paper ID : [E0568] [Note: Please fill

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Total No. of Questions : 08J . (Total No. of Pages: 03

.f"'o M. Tech.

INFORMATION THEORY AND CODINGSUBJECT CODE: EC -509

Paper ID : [E0568][Note: Please fill subject code and paper'ID on OMR]

Time: 03 Hours

Instruction to Candidates:

1) Attempt any Five questions.

2) All questions carry equal marks.

Maximum Marks: 100

Ql) (a) The spectrum of an analog audio signal is shown below; The waveformis to be sampled at a 10kHz rate with a pulse width of '"[=50microseconds.Find an expression for the spectrum of naturally samples PAM waveform.

. Sketchyour result.

W(f)

-4 4 f (KHz)---Ii>

(b) Show that uniform sampling of a signal in time domain results in a periodicspectrum in frequency domain. .

Q2) (a) Consider an audio signal with spectral components limited to frequencyband 300 to 3300 Hz. Assuming that sampling rate of 8000sample/secwill be used to generate a PCM signal. Assuming that ratio of peak power

,to average quantizer noise power at the output needs to.be 30 dB. Whatis the minimum number of uniform Quantization levels needed and whatis the minimum number of bits needed per sample? Derive the formula'used.

(b) Discuss the Delta Modulation in detail. Why Adaptive Delta Modulationis preferred over Delta Modulation.

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.Q3) (a) Differentiate between adaptive and predictive filters with the help of a

suitableexample. .

(b) Compare and explain the operations ofPCM, DPCM and OM. '--'

Q4) The signal component of a coherent PSK system is defined by

S (t) = Ack Sin(2 1tfct) + Ac ~1-k2 Cos(21t fct)

Where 0 < t < tb, and the plus sign corresponds to symbol 1 and minus signcorrespond to sYmbol o. The first term r~presents a carrier component includedfor the purpose of synchronizing the receiver with the transmitter. Show thatin the presence of Additive white Gaussian noise of zero mean power spectral

density.Ni2, the average probability of error is given by

'1

JE 1 I

~ =-erfc{ ~(1-k2)} where Eb =-k;Tb.2 No 2

. Q5) (a) Derive the relation to find the entropy of binary symmetric channel.

(b) Explain the concept of TDM. How signal rec~:>veryis done in a TDM, -

system.

Q6) (a) Compare and explain the oper~tions of M-aryPSK and M-ary FSKmodulation techniques.

(b) Explain the following.

(i) Shannon Fano theorem.

(ii) Linear block codes.

Q7) Suppose you need to use Huffman coding to encode the fol~owingmessage:spring, and the probability of appearance of each letter is given as following:

P(s)=O.2,P(P)=O.l P(r)-O.05 P(i)=O.6P(n)=O.02P(g)=O.03

(a) What is the entropy of this message source?

(b) Construct a Huffman tree.

. (c) What is the bitstream resulted from Huffman coding to represent theword?

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Q8) (a) Consider the binary block code C composed of the following fo~r codewords. ' '

- C={(00100), (10010), (01001), (11111)}

(i) What is the number of information bi~s,k?

(ii) What is the number of parity-check bits, c?

. (iii) What i~the minimum distance of this code?

(iv) What is the maximum weight for which the detection of all errorpatterns is guaranteed?

(v) What is the maximum weight for which the correction of all errorpatternsis guaranteed? .

(vi) Is th~scode linear? Prove your answer.

(b) Give the brief description of cyclic codes and how the parity checkmatrix can be generated for the cyclic codes.

0*0*

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