# Mumbai University Previous year question papers

## Digital Communication

N.S.: Ouestion No.1 is compulsory.

Solve any four questions from Q. Nos. 2 to 7.

Draw neat sketches, wherever necessary.

Assume suitable data, wherever necessary and justify  it.
Figures to the right indicate full  marks.

1.(a) For a binary memory source with two symbols m1 and m2,  show that entr0PY H(x) is maximum when both m1and m2 are equiprobable. What are the lower and upper bounds on H(x). ..

(b) Prove that for the 16-ary QASK digital modulation technique, the Euclidean distance is given by d=2.jO.4Eb

Where Eb is the normalized energy per bit.

(c) Define the following:

(i) Sampling theorem fo.:Bandpass signal.

(ii) Sampling theorem in frequency domain

(iii) Linear Siock codes.

2. (a) A message 101101 is to be transmitted using cyclic code having a generator polynomial g(x) = x4 + x3 + 1: Obtain the transmitted codeword. How many chec (parity) bits does the encoded message contain? Draw a suitable encoder arrangement ‘for the same.

(b) Derive an expression for signal to noise ratio of an integrate and dump filter and hence explain how the signal is emphasised relative to noise. What is the ideal output at the sampling time?

3. (a) For the convolutional encoder arrangement shown below, draw the state diagram and hence, the trellis diagram,.Determine the output sequence for the input data 11010100. What are the dimensions of the code and find its constraint length. Use Viterbi algorithm to decode the sequence

100110111

101001 101001010.

(b) Derive an expression for probability of error of an optimum filter.

4.(a) , A generator matrix of (6, 3) linear block code is given by :

‘ 0 0 , I ‘

G= 0 I 0 , , 0

0 0 I 0 I 1

Determine:

(i):All the code vectors

(ii) “dmin”for the above code

(iii) Error detection and correction capability

(iv) If the received sequence is 101101, determine the message bit sequence’,

(b) Explain MSK with the help of relevant expressions and waveforms. Sketch the PSD of MSK and QPSK and compare them. .

5. (a) The binary data  is applied to the input of a modified duobinary encoder:

(i) Construct the modified duobinary co’der output and corresponding receiver output without precoding.’ .

(ii) Suppose that due to error during transmission, the level produced by the third digit is reduced to zero. Construct the new receiver output. What should be done to avoid error prcp~gation ?

(b) In a fascimile transmission of a picture, thee are about 2.25 x 106 picture elements per frame. Twelve bright levels are requirEti for faithfull reception. Assuming all these levels equiprobable, calculate the channel bandwidth uquired to transmit one picture in every three minutes for a signal to noise power ratio of 30 dB. If ~1:\JR requirement is increased to 40 dB. calculate the new bandwidth. Comment on SNR-Bandwidth trade off, for the results obtained in above cases.

6.(a) Explain the transmitter and receiver of DEPSK system with block diagram, why error occur in pairs in DEPSK system? Give suitable example.

(b) A PN sequence is to be generated using a feedback shift register of length 4. The feedback taps is ‘given as (4. 1). Find the generated output sequence  if the initial contents of the shift register are 1000. If the chip rate is 101 Cilips/second. calculate:

(i) Chip duration and PN sequence duration.

(ii) Period of output sequence.

Also,draw its schematicarrangement.

7.(a) Compare the followng :

(i) Offset OPSK and non-offset QPSK.

(ii) Linear block  codes and convolution codes.

(b) Write short notes on (any two) :