MU Signal and Systems - December 2015 Exam Question Paper

MU Electronics Engineering (Semester 5)
Signal and Systems
December 2015

Total marks: --
Total time: --

INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) What is sinc(x) function? Plot graphically sinc(x) function for the range of x: -2.5

5 M

1 (b) Obtain DTFT and plot the magnitude and phase response of
h(n)={0, 1, 1, 1}

5 M

1 (c) Distinguish between power signals and energy signals. Is x(t)=cos²(w₀t) is energy signal or power signal? Find its normalized energy or power.

5 M

1 (d) State and prove differentiation of Z-transform.

5 M

1 (e) Check whether the following system is linear, time variant, casual or otherwise: y(n)=x(n)+n*x(n+1).

5 M

2 (a) Find the response of the system

x (t) = \frac{d^{2} y (t)}{d t^{2}} + 5 \frac{d y (t)}{d t} + 6 y (t)

$x(t)= \dfrac {d^2 y(t)}{dt^2} + 5 \dfrac {dy(t)}{dt}+ 6y(t)$ Subjected to the initial conditions y'(0)=2, y(0)=1 and input x(t)=e^-1 u(t).

10 M

2 (b) Find and sketch the Even and Odd components of the following:
x(t)=t, 0≤t≤1
x(t)=2-t, 1≤t≤2

5 M

2 (c) State and prove frequency shift property of the Fourier transform.

5 M

3 (a) Compute the convolution y(n)=x(n)*h(n) where X(n)={1, 1, 0, 1, 1} and h(n)={1, -2, -3, 4}.

8 M

3 (b) Find Inverse Z-transform of the following:

X (Z) = \frac{2 Z^{2} + 3 Z}{z^{2} + Z + 1}

$X(Z) = \dfrac {2Z^2 + 3Z}{z^2 + Z+1}$ if x(n) is causal.

8 M

3 (c) Define ESD and PSD. What is the relation of ESD and PSD with autocorrelation?

4 M

4 (a) Find y(t)=x(t)*h(t) of the signal shown above using graphical convolution.

10 M

4 (b) Obtain system function H(z) for

y (n) + \frac{1}{2} y (n - 1) = x (n) - x (n - 1)

$y(n) + \dfrac {1}{2} y(n-1)=x(n)-x(n-1)$ Determine the poles and zeros and draw a pole zero plot.

5 M

4 (c) Obtain DTFT and plot the magnitude and phase response of h(n)={2, 1, 2}.

5 M

5 (a) Determine the Z transform and sketch ROC.

1) x_{1} [n] = {[\frac{1}{3}]}^{n}; n \geq 0 2) x_{2} [n] = x_{1} [n + 4]

$1) \ x_1[n] = \left [ \dfrac {1}{3} \right ]^n; \ n\ge 0 \\ 2) \ x_2 [n] = x_1 [ n+4]$

10 M

5 (b) Obtain Laplace transform by using properties of Laplace transform only.

5 M

5 (c) Determine Fourier transform of signum signal.

5 M

6 (a) Obtain initial Laplace transform of

X (s) = \frac{2 s^{2} + 5 s + 5}{(s + 2) (s + 1)^{2}}

$X(s) = \dfrac {2s^2 + 5s+ 5}{(s+2)(s+1)^2}$ for all possible ROC conditions.

10 M

6 (b) Obtain Fourier transform by using properties of Fourier transform only.

10 M

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