Code No. 2096 / N

FACULTY OF ENGINEERING

B.E. 3/4 (Inst.) I-Semester (New) (Suppl) Examination, May 2013 Time : 3 Hours

Subject : Signals and Systems

Max. Marks: 75

Note: Answer all questions of Part - A and answer any five questions from Part-B. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

PART – A (25 Marks) List the properties of LTI systems. Consider a continuous time system with input x(t) and output y(t) related by y(t) = x2(t-2). Test, whether the system is linear or not. Define using example an orthogonal set. What are the necessary conditions for the existence of Fourier series. Find the Fourier transform of a Gate function. State the modulation property of a Fourier transform. State the initial value and find value theorem of lapalce transform. Determine the laplace transform of the x(t) = t 2 u(t). Find the z-transform of x(n)= {6, 7, 8, 9, 10,11}. What is Aliacing effect? How to eliminate it?

(2) (3) (3) (2) (3) (2) (3) (2) (2) (3)

PART – B (5x10=50 Marks) 11.(a) Find the output of a system with impulse response h(t) = e -3tu(t) and the I/P signal x(t)=u(t-3)-u(t-5). (5) (b) Explain in detail with examples the classification of a discrete time system. (5) 12.(a) Find the trigonometric Fourier series coefficients for the waveform shown in figure 1. (7)

Figure 1 (b) Write the equivalent exponential Fourier coefficient of figure 1 using their relations. (3) 13.(a) State and explain time and frequency convolution properties of Fourier transform.  1, t  0 (b) Find the Fourier transform of sgn(t )   1 t  0

(5) (5)

14.(a) Find the solution of the given differential equation using lapalce transform. (6) d2 d y (t )  7 y (t )  12 y (t )  0 2 dt dt Assume zero initial conditions. 1 (b) Determine the inverse lapalce transform of F ( s )  2 . (4) s ( s  1) 15. State and prove Sampling theorem. (10) 16.(a) State and proof any five properties of z-transform. (b) Find x(h), if its z-transform X(z) in given by X ( Z )  x(a) to be causal. 17.

Write short notes on the following: (a) Analogy between vector and signal (b) Convolution (c) Properties of Laplace transform *****

1 1  z '

(7) 1 2 z 2

assume (3) (5) (2) (3)

Vasavai CE B.E IT 3rd Year May 2013 Signals and Systems.pdf ...

(c) Properties of Laplace transform (3) *****. Page 1 of 1. Vasavai CE B.E IT 3rd Year May 2013 Signals and Systems.pdf. Vasavai CE B.E IT 3rd Year May 2013 ...

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