Amrita Vishwa Vidyapeetham 2009 B.Tech Electronics and Communications Engineering Signals and Systems internal 2 - Question Paper
Amrita Vishwa Vidyapeetham, Amrita School of Engineering Amritapuri Campus Signals and Systems
III Semester: ECE,EEE Second periodicals October 2008
Max. Marks: 50
Time: 2 hours
Answer all questions.
Q.1 x(t) * 8(t to) = ...
(2 marks) (2 marks)
(4 marks)
Q.2 Find the Fourier coefficient of
Q.3 Find the time domain signal corresponding to DTFS
r*i /4nk. , , ,6nk.
x [k\ = cos(1)+2 Jsin(-)
Q.4 Find the particular solution of the following differential equation
(4 marks)
4y(t)+5 d;y(t)+4y(t) = drtx(t) dt dt dt
d
y(0) = 0, y(t )|t=0 = 1, x(t) = sin(t )u(t)
Q.5 Find the total solution of the following difference equation
(5 marks)
y[n] 1 y[n 2] = x[n 1], y[1] = 1, y[2] = 0, x[n] = u[n]
Q.6 Draw the Direct form I and Direct form II form implementations of the following differential equations. (5 marks)
d2 d d d? ><' >+5 i,y(' >+4y(I ) = dtxtl >
Q.7 Find the step response of the following LTI systems represented by the following impulse response (4 marks)
h(t) = -(u(t) u(t 4))
Q.8 For each of the following impulse responses, determine whether the corresponding systems are (i)memroyless, (ii)causal and (iii)stable (6 marks)
(i) h(t) = e u(t 1)
(ii) h(t) = 38(t)
X(eja) = 1, |Q| < W
0, W < |Q| < n
Q.10 Find the inverse FT of X(j) = 2n8(a) (5 marks)
Q.11 Determine whether each of the following statements concernig LTI systems are True or false. Justify your answer (8 marks)
(a) If h(t) is the impulse response of the LTI system and h(t) is periodic and nonzero, the system is stable.
(b) if h[n] < k for each n, where K is a given number, then the LTI system with h[n] as its impulse response is stable.
(c) If an LTI system is causal,it is stable.
(d) The cascade of a noncausal LTI system with causal one is ncessarily noncausal.
Poorna S, Jinu Jayachandran Page 2 of 2
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