Anna University Coimbatore 2010 B.E Electronics & Communication Engineering 080290015- Signals and Systems - Question Paper
080290015- Signals and Systems its here in pdf format.....i written that examination in last month only...
ANNA UNIVERSITY OF TECHNOLOGY, COIMBATORE B.E. / B.TECH. DEGREE EXAMINATIONS : NOV / DEC 2010 REGULATIONS : 2008 THIRD SEMESTER - ECE 080290015 - SIGNALS AND SYSTEMS TIME: 3 Hours Max.Marks: 100
PART -A
(20 x 2 = 40 Marks)
ANSWER ALL QUESTIONS
1. Represent the unit step sequence u[n] in terms of linear combination of weighted shifted impulse functions
2. Find the fundamental period of the signal x(0 = s'n
3. Define Energy and Power signal
d2y(t) dy(t) _
4. Is the system ' ~ ' linear and time invariant?
5. Find'[2(a>)] ?
6. What is Region of Convergence?
7. Find the Laplace transform of
8. State and prove the time scaling property of Fourier transform
9. What is the necessary and sufficient condition on the impulse response for stability?
10. Define Transfer function.
11. Define state of a system.
5 + 2
12. Plot the pole zero diagram for the transfer function s2 +2s +2
13. State Sampling theorem.
14. Write any four properties of Region of convergence of the Z transform.
15. What is the overall impulse response h(n) when two systems with impulse
responses h, () & h2{n) are in series?
16. What are the different methods of evaluating inverse Z transform?
17. Find the convolution of the following sequence
x]() = {2-1,1,3}&x2() = {0,3,4,2}
18. Write the Discrete time Fourier transform pairs
19. Find *() when X = (z = Q 8)2
20. Find the transfer function H(2) of the system
y\n] - 0.5y\n -1] = x[ri\ + 03x[n -1]
PART -B
(5x 12 = 60 Marks)
ANSWER ANY FIVE QUESTIONS
21. Find the state variable matrices A,B,C and D for the equation
y(n) - 3y(n -1) - 2y(n - 2) = x(n) + 5x(n -1) + 6x(n - 2)
22. Check linearity, time invariance, causality and memory status of the systems
(i) y(n) = x(n)x{n -1) (ii) y(t) = 10x(t) + 5 (iii) y[n] = n x[n] (iv) y(t) = x(-t)
23. Find the Fourier series representation of the signal
t + 2 for - 2 < t < -1
1 for -\<t<\
x(t)
2 t for \ <t <2 0 for 2<t <3
24. The input and output of a causal LTI system are related by the differential d2y(t) , , dy(t)
2 +6 -8y(0 - 2x(t). What is the response of the system if
equation-
x{t) = te 2lu(t)
25. (a) Find the fundamental period of the following signals
(8)
(i) x{n) = sin 2m + sin 6m
/ N (
(ii) x(n) = 2 cosjJ + SlnJ -
..... x(t) = sin
(Ml) V '
v J y
(4)
(iv)x(/7) = sin In (b) State and prove any two properties of DTFT.
26. (a) Determine the inverse Z transform of X(2) - ~ when x(n) is
z -3z +2
causal
(6)
(6)
(b) Determine the inverse Z transform of
X(z) =---, ROC: Izl > 0.5
27. Find the solution to the following linear constant coefficient difference equation
3 1 (\ Y
y(n)- y(n-\) + y(n~2) = I ~ I for n - 0 with initial conditions
y(-1)=4 and y(-2)=10
28. Realize the following discrete time system function in cascade and parallel form
1
H{Z)-
*****!He END*
4
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