Signals And Systems Question Paper - Dec 16 - Electronics And Telecomm (Semester 4)

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Signals And Systems - Dec 16

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 the following

a) Determine if the following system is memoryless, casual, linear, time invariant

y(t) = t x(t)

(5 marks) 00

b) Explain in brief ROC(Region of Convergence) conditions of Laplace tranform.

(5 marks) 00

c) Explain Gibbs phenomenon. what is a Gibbs oscillation?

(5 marks) 00

e) Determine if the given sequence is periodic or not. If periodic, find out fundamental period

x[n] = sin($\frac{6\pi}{7}n +1$)

(5 marks) 00

a) Find the response of the time invarient system with impluse response h[n] = {1,2,3,1} using convolution as well as using transform. Verify your answers.

(10 marks) 00

b) Determine inverse Laplace Transform of

X(s) = $\frac{3x^2 + 8x + 23}{(x+3)(x^2 +2S +10)}$

(10 marks) 00

a) Detremine the Fourier transform of the trapezoidal function shown in the figure below:

(10 marks) 00

b) Find the inverse Z tranform of the following function

(10 marks) 00

X(z) = $\frac{1}{1 - 0.8z^{-1} + 0.12z^{-2}}$

for the following ROCs

a) |z| > 0.6

b) |z| < 0.2

c) 0.2 < |z| < 0.6

a) Find out DTFT of the following

(10 marks) 00

x[n] = {1,-1,-2,2}
x[n] = $-a^s$ u[-n-1], where |a|<1

b) An LTI system is described by the following equation. Determine the transfer function and impluse response of the system. Sketch the poles and zeros of the z-plane.

(10 marks) 00

y[n] - 4y[n-1] = x[n-1]

a) Find compact trigonometric fourier series for the signal x(t) shown in the following figure, Sktech the amplitude and phase spectra for x(t).

(10 marks) 00

b) The impluse response of a CT sytem is given below. Determine the unit step response of the system using convolution theorem of Laplace Transform.

(10 marks) 00

b(t) = u(t+2) + u(t-2)

a) A Ct signal has been shwon below. Sketch the following signals.

(10 marks) 00

i) x(t-4)

ii) x(4-t)

iii) x(-2t+2)

iv) x(0.5t)

b) State and proove with appropriate mathematical derivation, convolution in the time domain property and 'time reversal' property of Z transform. Also comment on importance of these properties in the field of communication and signal processing.

(10 marks) 00

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