R09 - December, 2011 - Regular Examinations - Set - 1.

B.Tech II Year - I Semester Examinations, December2011

SIGNALS AND SYSTEMS

(COMMON TO ECE, EIE, BME, ETM, ICE)

Time: 3 hours Max. Marks: 75

Answer any five questions

All questions carry equal marks

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1.a) Derive the expression for component vector ofapproximating the function f₁(t) over f₂(t) and also prove that thecomponent vector becomes zero if the f₁(t) and f₂(t) areorthogonal.

b) Arectangular function f(t) is defined by ???<<-<<=ppp2101)(tttf

Approximatethis function by a waveform sint over the interval (o, 2p) such that themean square error is minimum. [15]

2.a)List out all the properties of Fourier Series

b) Obtain the trigonometric Fourier series for thehalf wave rectified sine wave shown in Figure.1. [15]

Figure.1

3.Determine the Fourier transform for the double exponential pulse shown inFigure.2.

[15]

Figure.2

4.a)Define Linearity and Time-Invariant properties of a system.

b) Show that the output of an LTI system is given bythe linear convolution of input signal and impulse response of the system. [15]

5.a)State and prove Parseval’s Theorem.

b) Find the convolution of two signals x(n) = { 1, 1,0, 1, 1} and h(n) = { 1, -2, -3, 4} and represent them graphically. [15]

6.a)State and Prove the sampling theorem for Band limited signals.

b)Discuss the effect of aliasing due to under sampling. [15]

7.a)Define Laplace Transform and Its inverse.

b)Define Region of convergence and state its properties.

c)Find the Laplace transform of f(t) = sin at cos bt and f(t) = t sinat [15]

8.a)Find the two sided Z-transform of the signal x(n) = (1/3)ⁿ n = 0

= (-2)ⁿ n = -1

b) Determine the inverse Z-Transform of X(z) = z /(3z² – 4z 1), if the region of convergence are i) z > 1 ii) z < 1/3 iii) 1/3 <z < 1 [15]

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