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LOYOLA ICAM COLLEGE OF ENGINEERING AND TECHNOLOGY

(LICET)

LOYOLA COLLEGE CAMPUSNUNGAMBAKKAM, CHENNAI -34.

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

MODEL EXAMINATION OCT2011

Subject: Signals And Systems Duration : 3 hrs.

Sub. Code: 147303 Max marks : 100

Branch: ECE Date : 28/10/2011

Part A (10 x 2 = 18 marks)

1. Determine the power and RMS value of the signal x(t) = ejt cos0t.

2. If the discrete time signal x [n] = {0,0,0,3,2,1,-1,-7,6}. Find y(n)= x(2n-3).

3. State Dirichlet condition for Fourier service.4. Find Fourier transform of eat u(-t).

5. Determine the Laplace transform of x(t) = eatsin(t) u(t) .

6. State the frequency shifting property of Laplace transform.

7. State sampling theorem.

8. State the time shifting and frequency shifting properties of DTFT.

9. Find the Z- transform of the given data sequence,

x (n) = 1 ; 0 < n < 10

0 ; otherwise

10. Distinguish between IIR and FIR systems.

Part B (2 x 16= 32 marks)

Answer any two questions.

11.a) Consider a system shown in the figure below. Determine whether it is (16)

i) Memory less ii) causal iii) linear iv) time invariant v) stable

x(t) Multiplier

y(t)

Cos ct

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(OR)

b) i) Find the even and odd component of the following signals (10)

1) x(t) = cos t + sin t + cos t sin t

2) X[n] = { -2, 1, 2, -1, 3}

ii) Find the fundamental period of the following signals. (6)

1) x(t) = 2sin(3t+1) + 3sin (4t-1)

2) X[n] = ej(7/3)n

12.a) Find the fourier series expansion of the half wave rectified sine wave.

. . . . . . .

OR

b) Find the fourier transform of the following signals

i) e3t u(t)

ii) x(t) = cos 0t u(t)

iii) x(t) = e-t sin 5t u(t)

-2 - 0

x (t)

2 3

A

t

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13.a.)i) Realize the following differential equation as a Direct Form II structure

(10)

d3 y(t) / dt3 + 4 d2 y(t) / dt2 + 7 dy(t) / dt + 8 y(t) = 5 d2 x(t) / dt2 + 4 dx(t) / dt + 7 x(t)

ii) Find the state equations of a CT-LTI system described by (6)

d2 y(t) / dt2 + 3dy(t) / dt +2 y(t) = x(t)

(OR)

b) i) Find the convolutions of x(t) and h(t) for the following signal. (12)

ii) Find the convolutions of x1(t) = r(t) and x2(t) = e-2t u(t) for the following signal (4)

1 2 3-1

1

t

h(t)

1 2 3-1

1

t

x(t)

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Determine (1) Frequency response of the system.

(2) Impulse response of the system.

(ii) Determine h2(n) for the system shown in figure below.

15. a)i) Find the inverse z-transform of X(z) = { (z+1) / (3z2 4z + 1) }; |z | > 1 using

partial fraction expansion method. (8)

ii) Determine the z-transform for the signal x(n) = ( 2/3 )n u(n)+ ( -1/2 )n u(n)And plot the ROC and pole zero locations of X(z) (8)

(OR)b) i) Find the fourier transform of unit step sequence x(n) = u(n) . (8)

ii) Write a brief note about ALIASING and zero order hold circuit. (8)

H(ej) = -12 + 5 e-j

12 -7 e-j + e-j2

h1(n) = (1/3)n u(n)

h2(n) = ?

+x(n)