B.E-B.E Electronics and Communication Engineering Signals and Systems (Sathyabama University, Chennai, Tamil Nadu-2012)
Monday, 19 August 2013 07:29Duraimani
(Established under section 3 of UGC Act,1956)
Course & Branch :B.E - P-ECE
Title of the Paper :Signals & Systems Max. Marks:80
Sub. Code :SECX1004 (2011-2012) Time : 3 Hours
Date :05/11/2012 Session :AN
PART - A (10 x 2 = 20)
Answer ALL the Questions
1. Write any two properties of impulse.
2. Define energy and power signals.
3. Find the Fourier transform of the following signal x (t) = e2t u (t).
4. Find the Laplace transform and ROC of the following signal x (t) = – e-at u (-t).
5. Define transfer function of LTI system.
6. State the properties of convolution.
7. Consider an LTI system with impulse response h (n) = δ (n-no) for an input x(n), find Y(e jω ).
8. Define Region of convergence with respect to Z transform.
9. Consider an LTI system with difference equation y(n) - ¾ y(n-1)+ 1/8y(n-2)=2x(n). Find H (Z).
10. Find the discrete time Fourier transform of the following X (n) = .
PART – B (5 x 12 = 60)
Answer All the Questions
11. Explain the classification of signals with examples.
(or)
12. Find which of the following signals are Energy signals, power signals, neither energy nor power signals.
(a) X1 (t) = e -3t u(t) (b) X2 (t) = e j(2t + π/4)
(c)X3 (n) = (1/3)n (d) X4 (n) = cos (πn/4)
13. Discuss the properties of Fourier transform in detail.
(or)
14. (a) Find the inverse Laplace transform of the following X(s) = . (4)
(b) Use the convolution theorem of Laplace transform to find
y (t) = x1(t) * x2 (t) where x1(t) and x2(t) are as given below. x1(t) = e-3tu(t), x2 (t) = u(t-2) (8).
15. (a) Find the transfer function of the following
(i) An ideal Differentiator (ii) An ideal Integrator
(b) Find the forced response of the system with transfer function H(s) = for a unit step input.
(or)
16. Find the impulse and step response of the following systems H(s) =
17. (a)Compute the 4-point DFT of the sequence x(n) = 1, .
(b) Obtain the relation between Z transform and DTFT.
(or)
18. (a) State and prove any four properties of Z-transform.
(b) Find the inverse Z transform using contour integral method for given X(Z) = , .
19. (a) Consider an LTI system with the system function H(z) = , find the difference equation.
(b) Compute the convolution of the 2 sequences and plot the output x(n) = ; h(n)= (or)
20. Find the output sequence y(n) of the system described by the equation y(n) = 0.7y(n-1) – 0.1y(n-2) +2x(n) – x(n-2) for the input sequence x(n) = u(n).
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