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Signals And Systems Question Paper - Dec 17 - Electronics And Telecomm (Semester 4) - Mumbai University (MU)
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Signals And Systems - Dec 17

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 whether the following signals ar energy signals or power signals and calculate thier energy or power.
(5 marks) 00

  1. x(t) = $e^{-4t}u(t)$
  2. x(n) = $(\frac{1}{6})^n$(n)

b) Determine if following system is memory less, causal, linear, time invariant.
(5 marks) 00

y(t) = $a^n$x(n)

c) Using properties of fourier transform, detremine fourier transform of x(t)
(5 marks) 00

x(t) = $e^{-3|t-z0|}$ + $e^{3|t+z0|}$

d) Find out even and odd components of following signlas:
(5 marks) 00

  1. x(n) = u(n) - u(n-5)
  2. x(t) = 5 + 7t + 9$t^2$

e) Determine relation between contionus time fourier transform and laplace transform
(5 marks) 00

Q2)

a) Determine fourier series repersentation of following signal:
(10 marks) 00

b) Find impluse response and step response of continous time systems governed by following transfer functions.
(10 marks) 00

$H(s) =\frac{s+3}{s^2 + 6s +8}$

Q3)

a) A contionuos time signal is defined as,
(10 marks) 00

x(t) = t; 0<t<3</p>

x(t) = 0; t>3

sketch waveforms of following signals:

  1. x(-t)
  2. x(2-t)
  3. x(3t)
  4. x(0.5t +1)

b) Determine inverse z-transform of follwoing functions using long divison method:
(5 marks) 00

$X[z] =\frac{z^2 + 2z}{z^3 -3z^2 + 4z +1}$; ROC; |z| > 1

c) Compute the DTFT of sequence x(n) = {0,1,2,3}. Sketch magnitude and phase spectrum.
(5 marks) 00

Q4)

a) Using Laplace transform determine complete response of system described by following Equation.
(10 marks) 00

$\frac{d^2y(t)}{dt^2} +6\frac{dy(t)}{dt} +8y(t) = \frac{dx(t)}{dt} + x(t)$; where y(0) = 1;$\frac{dy(0)}{dt}$=3, for input x(t) = u(t)

b) Find impluse response of system described by following difference equation
(10 marks) 00

y(n) -$\frac{3}{4}y(n-1) + \frac{1}{8}y(n-2)$ = x(n) + x(n-1)

Q5)

a) For the following continuous time signals, determine fourier transform.
(10 marks) 00

  1. x(t) = $e^{-at}$ u(-t)
  2. x(t) = sin$\omega_0$(t) u(t)

b) Dtermine fourier series repersentation of x(n) = $4cos\frac{n\pi}{2}$
(5 marks) 00

c) Determine cross correlation of sequence x(n) = {1,1,2,2} and y(n) = {1,3,1}
(5 marks) 00

Q6)

a) The input signal x(t) and impulse response h(t) of a continuous time system are described as follows:

$ x(t) = e^{-3t} u(t) $ and $h(t) = u(t-1)$. Find output of system using convolution integral.

(10 marks) 00

b) Determine Z transform and ROC of

(i) $x(n) = n^2 \space u(n)$

(ii) $x(n) = a^n cos \omega_0 n \space u(n)$

(10 marks) 00

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