f(t) 0 1 2 3 t fig. q . 2 (b) - tgpcet · b) draw and explain block diagram of coherent and non...

NIR/KW/18/3357/3362 1 P.T.O

B.E. (Electronics Engineering / Elect. Telecommunication / Elect. Communication Engineering)

Fourth Semester (C.B.S.) Signals & Systems

P. Pages : 3 NIR/KW/18/3357/3362

Time : Three Hours Max. Marks : 80

_____________________________________________________________________

Notes : 1. All questions carry marks as indicated.

2. Solve Question 1 OR Questions No. 2.






8. Due credit will be given to neatness and adequate dimensions.

9. Assume suitable data whenever necessary.

10. Illustrate your answers whenever necessary with the help of neat sketches.

11. Use of non programmable calculator is permitted.

1. a) State and prove modulation theorem. Also explain its significance.

7

b) i) Find out Fourier Transform of signum function sgn(t).

3

ii) Find out Fourier Transform of osin w t .

OR

4

2. a) State and prove frequency differentiation property of Fourier Transform.

6

b) Using time differentiation property, find the Fourier Transform of the function shown in

fig. Q. 2(b).

f(t)

1

t2

0 1 2 3 t

Fig. Q. 2 (b)

8

3. a) A random experiment consists of drawing three cards from a deck in succession (without

replacing the first and second card drawn). Find the probability of obtaining three red aces

in three draws.

6

b) Define conditional, joint and independent probability. Find the relationship between them.

Differentiate between a random variable and random process.

OR

7

*1303*

NIR/KW/18/3357/3362 2

4. a) The joint probability function of two random variables x and y is given by

2f (x) C(x 2y); for x 0,1,2 and

y 1,2,3,4

0 ; otherwise

= + =

=

=

Find :

i) The value of C. ii) p(x 2, y 3)= = and

iii) p(x 1, y 2)

6

b) Prove that the auto – correlation function R( ) and power spectrum density S( ) forms a

Fourier transform pair.

7

5. a) The data 10110101 is to be transmitted. Draw the waveform for the following formats.

i) Unipolar RZ

ii) Polar NRZ

iii) Bipolar NRZ

iv) Bipolar RZ

v) Split Phase Manchester

10

b) Explain in brief the properties of line coding.

OR

3

6. a) Derive PSD in case of Bipolar signaling.

6

b) Explain intersymbol interference in detail. Explain how we can reduce ISI.

7

7. a) Explain the working principle of envelope detector for detection of AM wave.

5

b) Differentiate between SSB and DSB modulation techniques. Explain any one method of

DSB wave generation.

OR

8

8. a) State and explain A-law and law− .

5

b) Explain transmitter and receiver of Adaptive Delta modulation.

8

9. a) Explain in brief DPSK. Also explain coherent detection method of DPSK.

8

b) Write short note on M-ary communication system.

OR

5

10. a) Draw ASK, PSK and FSK waveform for the binary sequences :

i) 1100011

ii) 1010111

iii) 1111111

9

NIR/KW/18/3357/3362 3 P.T.O

b) Explain in brief, matched filter receiver.

4

11. a) A memoryless source emits six messages with probabilities 0.3, 0.2, 0.18, 0.15, 0.15 and

0.02 respectively. Find out binary Huffman code, code efficiency and redundancy for this

code.

7

b) For (6, 3) systematic, Linear Block Code, the generator matrix is given by

1 0 0 1 0 1

G 0 1 0 0 1 1

0 0 1 1 1 0

=

Find out corrected code vectors for the following received vectors.

r 101101,=

111011,

001101

OR

7

12. a) For a (7,4) non-systematic cyclic code, the generator polynomial is 3 2g(x) x x 1= + +

construct all the code vectors.

8

b) For the given convolution encoder, draw the code tree.

S S1 S2

++

V2 = S S2+

V1 = S S1 S2+ +

Data in

************

6

NIR/KW/18/3357/3362 4

TKN/KS/16/7360/7365 1 P.T.O

B.E. (Electronics Engineering / Electronics Telecommunication /

Electronics Communication Engineering) Fourth Semester (C.B.S.) Signal & Systems Paper - V

P. Pages : 2 TKN/KS/16/7360/7365


_____________________________________________________________________

Notes : 1. Same answer book must be used for both section.

2. All questions carry marks as indicated.


4. Assume suitable data wherever necessary.

5. Illustrate your answers wherever necessary with the help of neat sketches.

1. a) State and prove frequency convolution property of fourier transform.

6

b) Prove that fourier transform of a train of impulses is another train of impulses.

OR

8

2. a) State and prove sampling theorem.

6

b) State and prove time differentiation and frequency differentiation property of fourier

transform.

8

3. a) What are the properties of probability density function and cumulative distribution

function?

7

b) Differentiate between the random process and the random variable by giving suitable

examples of both.

OR

6

4. a) A room contain three sockets for bulbs. From the collection of bulbs out of which 4 are

defective, 3 bulbs are selected at random and put in sockets.

Find the probability that room is lit.

5

b) The probability density function is given as |x|aexF bx

,

Where X is random variable whose allowable values range from - to .

Find i) Relationship between a and b.

ii) 2x1P .

8

5. a) Derive the PSD of on-off signaling.

6

b) State and explain Nyquist First criterion for zero ISI.

OR

7

6. a) Digital data 1101001011 is to be transmitted. Draw waveforms for following methods.

i) Unipolar NRZ ii) Bipolar RZ

iii) Manchester iv) Polar RZ

8

b) What is line coding? What are the properties of line coding.

5

7. Explain delta modulation with transmitter and receiver. Differentiate between delta

modulation and adaptive delta modulation.

OR

13

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TKN/KS/16/7360/7365 2

8. a) Explain square law demodulator

7

b) Explain threshold in FM.

6

9. a) Explain Differential phase shift keying.

5

b) Draw and explain Block diagram of coherent and Non-coherent FSK.

OR

8

10. a) Write a short note on 'M-ary communication system'.

4

b) Draw ASK, FSK & PSK waveform for following binary sequence.

i) 101101 ii) 0111001

ii) 001011

9

11. Construct a systematic (7,4) cyclic code using generator polynomial 1xxxf 3 .

What are error correcting capability of this code? Construct the decoding table. If the

received word is 1101100, determine the transmitted data word.

OR

14

12. a) Show that the channel capacity for a continuous channel is given by.

sec/bitsN

S1logBC 2

6

b) A binary channel matrix is given by

10

9

10

1

3

1

3

2

x

xInput

YY

output

2

1

21

3

2xP,

3

1xP 21

Determine : H (x), H (x/y), H (y), H (y/x)

8

*********

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KNT/KW/16/7272/7277 1 P.T.O

B.E. Fourth Semester (Electronics Engineering / Electronics Telecommunication Engineering /

Electronics Communication Engineering) (C.B.S.)

Signals & Systems Paper - V P. Pages : 3 KNT/KW/16/7272/7277


_____________________________________________________________________











11. Use of non-programmable calculator is permitted.

1. a) State and prove scaling property of Fourier Transform. What is the physical significance

of this property?

6

b) Find Fourier transform for given function.

i) Double sided exponential signal. ii) U (t) Cos wot.

OR

7

2. a) Find out Fourier Transform of the following function.

A

f(t)

0 1 2 3 4 5 6 7 8 t

8

b) Find inverse Fourier Transform of.

i) w ii) wow

5

3. a) If a function f (t) is given as f (t) = A cos wot then find out

i) Auto correlation function. ii) Power spectral density.

6

b) What is the difference between ensemble and time average? State the conditions for a

process to be stationary, wide sense stationary or ergodic.

OR

7


KNT/KW/16/7272/7277 2

4. a) A Rayleigh density function is given by

Find : i) Fx(x)

ii) P (0.5 < x < 2)

8

b) A random experiment consists of drawing two cards from a deck in succession. Assign a

value to the probability of obtaining two red aces in two draws.

5

5. a) Derive the expression for power spectral density of NRZ Bipolar signaling and draw the

PSD characteristics.

7

b) Explain in brief Inter Symbol Interference (ISI). How we can reduce ISI?

OR

7

6. a) The data 10101101 is to be transmitted. Draw the waveforms for the following signaling

methods.

i) Unipolar NRZ ii) Polar RZ

iii) Bipolar RZ iv) Split phase Manchester

8

b) What is line coding? Explain properties of line coding.

6

7. a) What is single side band modulation technique? Explain phase shift method to generate

SSB signal.

7

b) Explain FM threshold effect in detail.

OR

6

8. a) Write detailed notes on any two.

i) Envelop detector & square Law demodulator.

ii) Delta modulation system.

iii) A - law and - law Companding.

iv) Pulse code modulation.

13

9. a) Draw ASK, PSK and FSK waveforms for the following sequences.

i) 11110000

ii) 10101010

iii) 10111010

9

b) Write short notes on M-ary communication systems.

OR

4

0x;0

0x;xexfx 2

2x

NagpurStudents.Org

KNT/KW/16/7272/7277 3 P.T.O

10. a) What is differential PSK? Explain DPSK with suitable block diagram. Discuss advantages

and disadvantages of DPSK system.

8

b) Write a short note on matched filter detection of binary signals.

5

11. a) A Zero memory source emits six messages with probabilities 0.3, 0.25, 0.15, 0.12, 0.1 and

0. 08. Find the quaternary Huffman code for this source as well as calculate code

efficiency and the redundancy.

7

b) For a (6,3) systematic Linear Block code, the generator matrix is given by

111

101

011

100

010

001

G

Construct the code generated by this matrix and determine the error correcting capabilities

of this code.

OR

7

12. a) For a (7,4) cyclic code, the generator polynomial is given by .1xxxg 23 Find all

corrected vectors for the following received vectors.

i) 1011001

ii) 1010111

iii) 1111111

iv) 0101101

8

b) For the convolutional encoder shown below, draw the code tree and state table.

+ +

S S1 S2

1 2

Datain

6

**************

NagpurStudents.Org

KNT/KW/16/7272/7277 4

NagpurStudents.Org

NRJ/KW/17/4412/4417 1 P.T.O

B.E. (Electronics Engineering / Elect. Telecommunication / Elect. Communication Engineering)

Fourth Semester (C.B.S.) Signals & Systems

P. Pages : 2 NRJ/KW/17/4412/4417


_____________________________________________________________________












1. a) State and prove time convolution property of Fourier transform.

6

b) Find Fourier transform of

i) Signum function ii) Double sided exponential signal.

8

OR

2. a) Find inverse Fourier transform of :

i) )w( ii) )ww( 0

5

b) State and prove time shifting property of Fourier transform.

4

c) Prove that Fourier transform of a train of impulses is another train of impulses.

5

3. a) Consider the following function 2/x2/;xcosk)x(f Find k such that the

function qualifies as probability density function.

6

b) Explain Auto co-relation and cross correlation functions. 7

OR

4. a) Explain power spectral Density and Energy spectral Density functions.

7

b) A coin is tossed four times in succession. Determine the probability of obtaining exactly

two heads.

6

5. a) Digital data 10101101 is to be transmitted. Draw the waveforms for the following

signaling methods.

i) Bipolar RZ ii) Polar NRZ

iii) Unipolar RZ iv) Split phase Manchester.

8

b) Explain the necessity of line coding. Also explain its properties. 5

OR

6. a) Explain the relationship between Bandwidth and Rate of Pulse transmission.

6

b) Explain Pulse spreading and Inter symbol Interference.

7


NRJ/KW/17/4412/4417 2

7. a) Draw and explain the Block diagram of PCM Transmitter and Receiver.

8

b) Explain A law and law. 5

OR

8. a) Write short note on Delta modulation and Adaptive Delta modulation.

8

b) Explain envelope Demodulation technique in detail.

5

9. a) Explain in brief the digital carrier modulation schemes. Draw ASK, FSK & PSK

waveforms for binary sequence

1) 10110101 & 2) 11100011

7

b) Write a short note on M-ary communication. 6

OR

10. a) Write a short note on DPSK system.

6

b) Draw and explain the Block diagram of coherent and non coherent FSK system

7

11. a) A zero memory source emits six messages with probabilities 0.30, 0.25, 0.15, 0.12, 0.10 &

0.08 find 4-ary i. e. quaternary Huffman's code. Determine its average word length, &

redundancy.

6

b) Binary channel have probabilities as shown in fig.

x1

x2

y1

y2

0.7

0.3 0.1

0.9

Determine all the entropies associated with the system. Assume

7.0)x(p&3.0)x(p 21

8

OR

12. a) A (6, 3) Linear Block code system have parity part given below:

011

101

110

P

Find all the codes of the system.

6

b) For the given convolution encoder, draw the code tree, state diagram and trellis diagram.

+ +

m1 m2 m3

1 2

I/P

8

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NagpurStudents.Org

NJR/KS/18/4412/4417 1 P.T.O

B.E. (Electronics Engineering / Elect. Telecommunication /

Elect. Communication Engineering) Fourth Semester (C.B.S.) Signals & Systems

P. Pages : 3 NJR/KS/18/4412/4417


_____________________________________________________________________












1. a) State and prove time convolution and frequency convolution property of Fourier

Transform.

8

b) Find Fourier Transform of :

i) Gate Function

ii) Double sided exponential signal.

OR

6

2. a) State & Prove scaling property of Fourier Transform. What is the physical significance of

this property.

7

b) Prove that Fourier Transform of a train of impulses is another train of impulses.

7

3. a) Explain the meaning of CDF and PDF. Also explain their properties.

7

b) A room contains three sockets for bulb. From the collection of bulbs out of which 4 are

defective, 3 bulbs are selected in random and put in sockets. Find the probability that the

room is lit.

OR

6

4. a) Consider the following function f (x) kcosx; / 2 x / 2= − . Find k such - that the

function qualifies as probability density function.

6

b) Explain auto co-rrelation and cross co-rrelation functions.

7

5. a) Explain the necessity of line coding also state its properties.

5


NJR/KS/18/4412/4417 2

b) Digital data 01101001 is to be transmitted. Draw the wave forms for the following

signaling methods :

i) Bipolar NRZ ii) Unipolar RZ

iii) Polar RZ iv) Split phase Manchester

OR

8

6. a) Explain Nyquist first criterion for zero inter - symbol interference.

7

b) Explain the relationship between bandwidth and rate of pulse transmission.

6

7. a) Draw and explain the block diagram of PCM encoder.

7

b) Compare Delta modulation and Adaptive Delta modulation systems.

OR

6

8. Write short notes any two :

i) A law and law companding.

ii) Pulse code modulation.

iii) Envelope Detector & Square Law Demodulator.

iv) Delta Modulation systems.

13

9. a) Draw ASK, PSK and FSK waveforms for the following sequences :

i) 1101 0100

ii) 01101001

iii) 01010101

9

b) Explain the need of modulation also define ASK, FSK & PSK.

OR

4

10. a) Write a short note on M-ary communication.

6

b) Explain DPSK with suitable block diagram. Discuss advantages and disadvantages of

DPSK system.

7

11. a) A zero memory source emits six messages with probabilities 0.30, 0.25, 0.15, 0.12, 0.10 &

0.08. Find 4 - ary i.e. quaternary Huffman's code. Determine its average word length ,

& redundancy.

7 NagpurStudents.Org

NJR/KS/18/4412/4417 3 P.T.O

b) The generator matrix for a (6, 3) block code is given below. Find all code vector of this

code.

1 0 0 : 1 1 0

G 0 1 0 : 0 1 1

0 0 1 : 1 1 1

=

.

OR

7

12. a) Discrete memoryless channel is shown in figure :

0.7

0.3

1

0.2

0.8

x1

x2

x3

y1

y2

y3

Calculate all entropies H(x), H(y), H(x / y), H(y / x), H(x, y) if

1 2 3P(x ) 0.3, P(x ) 0.4, P(x ) 0.3= = =

10

b) Calculate capacity of Gaussian channel with a bandwidth of 1 MHz & S/N Ratio of 20 dB.

************

4

NagpurStudents.Org

NJR/KS/18/4412/4417 4

NagpurStudents.Org

NKT/KS/17/7272/7277 1 P.T.O

B.E.Fourth Semester (Electronics / Electronics Telecommunication / Electronics

Communication Engineering) (C.B.S.) Signals & Systems

P. Pages : 3 NKT/KS/17/7272/7277


_____________________________________________________________________












1. a) What is the purpose of Fourier series ? Evaluate the trigonometric Fourier series

expansion of a full wave rectified cosine function shown in fig. Q. 1 (a)

0

2

5

2

3

2

2

2

3

2

5

2

7t

Fig. Q.1(a)

f (t)

7

b) What is the condition of existence of Fourier transform ? Find the Fourier transform of RF

pulse shown in fig. Q. 1(b) if it exists.

t

f(t)

0

Fig. Q.1(b)

7

OR

2. a) What is frequency shifting property ? Explain the significance. Find the Fourier transform

of coswct.

6

*0309* NapurStudents.Org

NKT/KS/17/7272/7277 2

b) State and prove frequency convolution & time convolution property of Fourier transform.

8

3. a) A town has a population of 10,000 people of these 6000 are males & 4000 are females.

Also 300 males and 400 females of this population are unemployed. An unemployed

person is chosen at random. What is the probability that he is male ?

6

b) The probability density function is given as |x|bx ae)x(f where x is r.v. whose

allowable values range from to . Find -

i) Relation between a and b

ii) )2x1(P

8

OR

4. a) What is the difference between time average and ensemble ? How random variable differs

from random process ? How will you identify an ergodic process ?

8

b) Determine the PSD and mean square value of the random process

)twcos(A)t(x c

where is an RV uniformly distributed over )2,0( .

6

5. a) Derive the PSD of unipolar signaling.

7

b) What is line coding ? Why is it necessary ? Explain the properties of line coding.

6

OR

6. a) The data 10101011 is to be transmitted draw the waveforms for -

i) Unipolar RZ & NRZ

ii) Polar RZ & NRZ

iii) Bipolar RZ & NRZ

iv) Split phase Manchester

7

b) What is ISI ? Now Nyquist achieved zero ISI in his first criterion ?

6

7. a) Why A-law & -law componding is employed ? explain in detail.

7

b) How delta modulation differs from adaptive delta modulation ? Explain.

6

OR

8. a) What is amplitude modulation ? Derive the expression for AM signal. Consider carrier as

Vc coswct. What is the range of modulation index in AM ?

6

b) What is frequency modulation ? Explain threshold effect in FM.

7

9. a) Draw the ASK, PSK and FSK waveform for -

i) 11001100

ii) 10011001

iii) 11110000

9

b) Explain many communication system.

4

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NKT/KS/17/7272/7277 3 P.T.O

OR

10. a) What is the difference between matched filter and correlation detector.

6

b) What do you understand by decision threshold and probability of error in matched filter.

7

11. a) The generator matrix for a(6, 3) block code is given below. Find all code vectors of this

code.

111001

011010

110100

G

5

b) The generator polynomial of a (7, 4) cyclic code is g(x) = 1 + x + x3. Find any 08 codword

of this code.

8

OR

12. a) A memoryless source emits six messages with probabilities 0.3, 0.25, 0.15, 0.12, 0.1 and

0.08. Find the 4-ary (quaternary) Huffman code. Determine the average word length, the

efficiency & redundancy.

6

b) Discrete memory channel is shown in the figure with 3 input and 3 output symbols.

X1

X2

X3

Y1

Y2

Y3

0.8

0.2

1

0.3

0.7

Fig. Q.12(b)

Calculate all entropies i.e. H(x), H(y), H(x, y), H(x/y) and H(y/x) if

P(x1) = 0.3, P(x2) = 0.4 and P(x3) = 0.3

7

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f(t) 0 1 2 3 t fig. q . 2 (b) - tgpcet · b) draw and explain block diagram of coherent and non...

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