Data Communication (IE30006)Department of Electrical Engineering

End-Semester examination (Spring, 2017-2018)

Date: 26-04-201 (F. 1\.)

Instruction: Answer all questions

Total marks: 50 Total time: 3 hoursQl. (a) The input to an envelope detector is a single tone amplitude modulated signal

,'CAJIf(t) = A(l + ~(COswn,l.) coswel where ~I is a constant and We »W1II

.

Show that is the detector output is to follow the envelope of XA,\I(l), it is required that at anytime to

1 ({lSinwmto)->wmRC - 1+ {LCOSWmlo

(4 marks)

(b) Mathematically analyze separately the effect of the local carrier signal in a DSB-SC syn-chronous demodulator being

(i) out of phase and(ii) mismatched in frequency.

(2 2 marks)

Q2. (a) Draw the block diagram of a super-heterodyne Al\I receiver and explain the utility ofeach of its components. What arc "image frequencies" ? How arc they suppressed?

(2+2 marks)

(b) Beginning from the spectra of DSB-SC mocl ulation , mathematically deri ve the tirne-domai nexpre sion for single sideband modulated waveform. ¢SSB(t) = m(l) coswcL 1=mh(L) sin weL

(4 marks)

Q3. (a) Compare and contrast the performance of FM and AM in the presence of n011-linearities of the channel. Mathematically justify that FM is more robust than AM in the presenceof non-linearities.

(3 marks)

------ ----------------

(b) Consider an angle modulated signal

x(t) = 10 cos[(108)7TL + 5 sin 27T(103)t]

Find the maximum phase deviation and the maximum frequency deviation.(3 marks)

Q4. (a) Consider a signal m(t) = cos(wot), where Wo = 27Tfo. Derive mathematically anddraw diagrams to show the reconstructed signal after under-sampling of m(t) when the samplingrate is Is = (3/2)10'

(3 marks)

(b) Find the Nyquist sampling rate for each of the following signals:(i) sinc( 1007Tt)+3sinc2 (6071 L)(ii) sinc(507Tt).sinc(1007Tt)

(3 marks)

Q5. (a) Prove that for uniform quantization the mean square value or power ofthe quantizationnoise is given by

~ 6.v2q2(t) =N =-

q 12where 6.v denotes the size of each quantization level.

(3 marks)

(b) A signal bandlimited to 3 kHz is sampled at 33~% higher than the Nyquist rate. Themaximum quantization error is 0.5% of the peak signal amplitude ttu; The quantized samples arebinary coded. Find the minimum bandwidth of a channel required to transmit the encoded binarysignal. If 24 such signals are time division multiplexed, determine the minimum transmissionbandwidth required to transmit the multiplexed signal.

(5 marks)

Q6. (a) What is inter-symbol interference (ISI)? Why does it occur? Consider a signal g(t)as shown below which is band-limited to B Hz.

t--

Assume that it is passed through a channel which has a frequency response given as

H(w) = { ~1kcos(wT))e-jwtd Iwl < 27TB

Iwl > 27TR

Plot the output signal y(t) and comment upon its nature. (4 marks)

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(b) Draw the detailed block diagram of a baseband binary data transmission system. Mathe-matically analyze and.show that typically inter-symbol interference (ISI) affects the transmissionof data ill such discrete pulse amplitude modulation (PAM) systems. Derive mathematically theoptimum pulse shape such that a Nyquist channel can he obtained-in which ISI is avoided.

. \~ (2+2+3 marks)~~~

.,

Q7. Consider the si-gnal s(t) shown in the Figure below

o T2

."r'

,~;\.,

s(I)

T

-~1----'---'2

(i) Determine the impulse response of a filter matched to this signal and sketch it.(1.5 marks)

(ii) Plot the matched filter output as a function of time.(1.5 marks)

3