## December 17, 2011

### SIGNALS AND SYSTEMS JNTU previous years question papers

SIGNALS AND SYSTEMS JNTU previous years question papers

Time: 3 hours Max Marks: 75
All Questions carry equal marks

1. (a) Evaluate the following integrals:
i.
R8
&1
[u(t + 3) & 2f(t):u(t)]dt
ii.
5
R2
1
2
f(3t)dt
(b) A even function g(t) is described by
g(t) =
8<
:
2t
15 & 3t
&2
0 f t < 3
3 f t < 7
7 f t < 10
i. What is the val ue of g(t) at time t = 5
ii. What is the val ue of 1st derivative of g(t) at time t = 6. [8+7]

2. (a) Distinguish between Energy and Power signals.
(b) Derive the expression for Energy density spectrum function of a energy signal f(t) from fundamentals and interpret why it is called Energy density spectrum.[5+10]

3. (a) Explain the concept of generalizedFourier series representation of signal f(t).
(b) State the properties ofFourier series. [8+7]

4. (a) Explain the properties of the ROC of Z transforms.
(b) Z transform of a signal x(n) ifX(z) = 1+z&1
1+ 1
3z&1 .
Use long division method to determine the val ues of
i. x, x, and x, assuming the ROC to be jzj > 1
3
ii. x, x[-1], and x[-2] , assuming the ROC to be jzj < 1
3 . [7+8]

5. (a) A signal y(t) given by y(t) = C0 +
1P
n=1
CnCos(n!0t + fn). Find the autocorrelation and PSD of y(t).
(b) Explain the Graphical representation of convolution with an example. [8+7]

6. (a) Consider anLTI system with input and output related through the equation.
y(t) =
Rt
&f
e(t&f)x(f & 2)dfWhat is the impulse response h(t) for this system.
(b) Determine the response of this system when the input x(t) is as shown
(c) Consider the inter connection ofLTI system depicted in fgure 6c.
Here h(t) is an in part (a). Determine the output y(t) when input x(t) is again given fgure above, using the convolution integral. [5+5+5]

7. (a) Consider the signal x(t) = (sin 50 ft / ft)2 which to be sampled with a sampling frequency of !s = 150 f to obtain a signal g(t) withFourier transform G(j! ). Determine the maximum val ue of !0 for which it is guaranteed that
G(j!) = 75 X(j!) for j!j (b) The signal x(t) = u(t + T0) - u(t - T0) can undergo impulse train sampling without aliasing, provided that the sampling period T< 2T0 . Justify.[7+8]

8. (a) Explain the method of determining the inverse Laplace transforms using Partial fraction method, for the following cases
i. Simple and real roots
ii. Complex roots
iii. Multiple or repeated roots.
(b) Find the Laplace transform of the function
f(t) = A Sin !0t for 0 < t < T/2. [3+3+4+5]

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