## SIGNALS AND SYSTEMS JNTU previous years question papers

Time: 3 hours Max Marks: 75

All Questions carry equal marks

1. (a) Write short notes on "Ideal BPF".
(b) In the following network, determine the relationship between R's and C's in order to have a distortion less attenuation while signal is transmitted through the network shown in fgure 1b. [8+7]

2. (a) State the three important spectral properties of periodic power signals.
(b) Determine theFourier series of the function shown in fgure 2b. [5+10]

3. (a) With the help of graphical example explain sampling theorem for Band limited signals.
(b) Explain briey Band pass sampling. [8+7]

4. (a) Find the Z-transform and ROC of the signal
x(n) = [4(5n) & 3(4n)] u(n)
(b) Find the Z-transform as well as ROC for the following sequences: [7+8]
i.
&1
3
fn
u(&n)
ii.
&1
3
fn
[u(&n) & u (n & 8)]

5. (a) State the properties of the ROC of Laplace transforms.
(b) Determine the function of time x(t) for each of the following laplace transforms and their associated regions of convergence. [7+8]
i. (s+1)2/ s2-s+1 Re fSg > 1/2
ii. s2- s+1/ (s+1)2 Re fSg > -1

6. (a) The rectangular function f(t) in fgure 6a is approximated by the signal 4fSin t.show that the error function fe(t) = f(t)-4/f Sin t is orthogonal to the function Sin t over the interval (0,2f).
(b) Determine the given functions are periodic or non periodic.
i. a Sin 5t + b cos 8t
ii. a Sin (3t/2) + b cos (16t/15) + c Sin (t/29)
iii. a cos t + b Sin
p
2t
Where a, b, c are real integers. [10+5]

7. (a) Determine theFourier Transf or m of a trapezoidal function and triangular RF
pulse f(t) shown in fgure 7a. Draw its spectrum.
(b) Using Parsevals theorem for power signals, Evaluate
f R
&f
e&2tu(t)dt. [10+5]

8. (a) Consider an input x[n] and an impulse response h[n] given by
x[n] =
&1
2
fn&2
u[n & 2];
h[n] = u[n + 2]:
Determine and plot the output y[n] = x[n] f h[n].
(b) Bring out the relation between Correlation and Convolution.
(c) Explain the properties of Correlation function. [7+4+4]

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