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 f_{1}(t) over f_{2}(t) and also prove that thecomponent vector becomes zero if the f_{1}(t) and f_{2}(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 TimeInvariant 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 Ztransform of the signal x(n) = (1/3)^{n }n = 0
= (2)^{n }n = 1
b) Determine the inverse ZTransform of X(z) = z /(3z^{2 }– 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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CreatedSep 29, 2012

UpdatedSep 29, 2012

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