Signals And Systems Question Paper - Dec 18 - Electronics And Telecomm (Semester 4)

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Signals And Systems - Dec 18

Electronics And Telecomm (Semester 4)

Total marks: 80
Total time: 3 Hours INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.

Q1 Answer any 4 questions from the given questions:

a) Find even and odd part of following continuous time signals

(5 marks) 00

X(t) = 3 + 2t + 5$t^2$
$x_2(t) = sin2t + cost + sintcos2t$

b) Determine energy and power of the unit step signal

(5 marks) 00

c) Explain the application of signals and system in multimedia processing.

(5 marks) 00

d) Construct the block diagram of discreate time systems whose input output realtions are described by following difference equations

(5 marks) 00

$Y_1(t)$ = 0.5x(n) + 0.5x(n-1)
$Y_2(t)$ = 0.25$y_1$(n-1) + 0.5x(n) + 0.75x(n-1)

e) Test the given system for linearity, casuality, stability, memory and time variant.

(5 marks) 00

y(t)=x($t^2$)

f) Give advantages of state space analysis for systems analysis.

(5 marks) 00

Q2 Perform convolution of $x_1(t) = e^{-3t}$ u(t) and $x_2(t)$ = tu(t) using mathematical method and also by graphical method.

(20 marks) 00

a) Dtermine the sequnce x[n] associated with Z-tranform

(10 marks) 00

X(z) = $\frac{1}{1-1.5z^{-1}+0.5z^{-2}}$

b) Find the impluse response h(n) of the system if the spectrum is given by

(10 marks) 00

$H(E^{jw}) = \frac{1}{3}$ (1 + cosw)

a) Explain the procedure to obtain transfer function of system from state model of the system.

(10 marks) 00

b) Find exponential Fourier series of x(t)

(10 marks) 00

a) Determine Fourier transform of gate function given by x(t) A for |t< $\frac{t}{2}$

(8 marks) 00

b) Find laplace transform of x(t) = u(t) - u(t-a)

(4 marks) 00

c) Find initial and final value using laplace transform.

(8 marks) 00

X(s) = $\frac{7s+6}{s(3s+5)}$

Q6 Write short note on any two:

a) Relation of ESD, PSD with auto-correlation

(10 marks) 00

b) ROC in Z-transform and laplace transform

(10 marks) 00

c) Feedforward control system.

(10 marks) 00

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