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

- - -

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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