SRM University 2007 B.Tech Electronics and Communications Engineering BANK : Signals and Systems - Question Paper

23. Say whether the subsequent system with impulse response h(t) is stable or not
i) h(t) = t e-t u (t) ii) h(t) = e-2t u (t-1)
24. Find the step response of the system. Whose impulse response is provided by h(t) = t u (t).
25. How can an arbitrary signal out can be represented as a linear combination of a scaled and shifted impulse functions.
26. What is the condition for a LTI CT system to be causal?
27. State duality property of Fourier transform.
28. State modulation property of Fourier transform.
29. Find the frequency response of an LTI-CT system defined by
30. If and LTI-CT systems frequency response is H (j ?) = a-j ? / a+j?. obtain |h(j?)|, H(j?) and impulse response.
31. State time convolution property of Fourier transform.
32. Given the transform pair L [x (t)] = 2s/s2 –2. Determine the Laplace transform of x (2t).
33. obtain the impulse response of H (s) = s+2/s2 + 5s + 4.
34. Find the transfer function of a ideal integrator.
35. State frequency shifting property of laplace transform.
36. Plot pole – zero diagram of the subsequent transfer functions.
1) s+2 / s2 +2s +2 2) S + three / s (s2+4) (s+2) (s+1)
37. What is meant by state of a system?
38. What is need of transforms in signal analysis?
39. Represent an inductor in s-domain with zero initial conditions.
40. What is the laplace transform of t n e-at.

Part – B

1. The input and output of an LTI-CT causal system is
d2y(t)/dt2 + six dy(t)/dt + eight y(t) = 2x(t)
i) What is the impulse response of the system.
ii) What is response of the system if x (t) = t-2t u(t)

2. Use convolution theorem of laplace transform obtain y (t) when
a) x1 (t) = e – 3t u (t) x2 (t) = u (t-2) b) x1 (t) = Cos 4t u(t) x2 (t) = sin2t u(t).

3. An LTI – CT system is defined by
d2y(t)/dt2 + five dy(t)/dt + six y(t) = dx(t)/dt + 4x(t)
The input is x (t) = e –t u(t)
obtain
1) Natural response for initial conditions y (0) = 3; dy (o)/ dt = 0
2) Forced Response 3) Total Response.

4 a) obtain whether the system is stable or not.
a ) h (t) = sin wot u (t).
b) obtain step response of h (t) = (t) – (t-1)
c) obtain convolution for x1 (t) = sin u (t) ; x2 (t) = u (t)

5. Using graphical procedure fine the convolution of the subsequent signals
x1 (t)= = e- 2t u (t); x2 (t) = u (t+2)

6. For a transfer function H (s) = S+10/ s2 + 3s + 2.
obtain the response due to input x (t) = Sin2(t) u (t).

Earning:   Approval pending.