R09 - December, 2011 - Regular Examinations - Set - 4.

B.Tech II Year - I Semester Examinations, December 2011
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) Approximate the function f(t) by a set of Legendre polynomials and derive the expression for component vector.
b) Define the following basic signals with graphical representation
i) Unit Sample Signal ii) Unit Step Signal
iii) Ramp Signal iv) Sinusoidal signal. [15]
2.a) Expand the following function over the interval (-4, 4) by a complex Fourier Series
f(t) = 1 ; -2 = t = 2
= 0 ; else where
b) Justify the following with respect to Fourier series
i) Odd functions have only sine terms
ii) Even functions have only cosine terms. [15]
3.a) Compute the Fourier Transform of
i) f(t) = (1/2)-n u(-n-1) ii) f(t) = sin(np/2) cos(n)
b) State all the properties of Fourier Transform. [15]
4.a) Draw the ideal characteristics of Lowpass, Highpass, Bandpass and Bandstop filters.
b) Test the linearity, causality, time-variance of the system governed by the equation
i) y(n) = x(n-n0) ii) y(n) = cos(n?0) x(n) iii) y(n) = a[x(n)]2 b [15]
5.a) Explain the process of detection of periodic signals by the process of correlation.
b) Determine the cross correlation between the two sequences x(n) = [1,0,01) and
h(n) = { 4,3,2,1} [15]
6.a) Define Nyquist rate. Compare the merits and demerits of performing sampling using impulse, Natural and Flat-top sampling techniques.
b) Discuss the process of reconstructing the signal from its samples. [15]
7.a) Bring out the relationship between Laplace and Fourier Transform.
b) Determine the Laplace transform of
i) f(t) = e-at sin ?t ii) f(t) = e-at cosh ?t
c) Find the final value of the function F(s) given by (S-1) / S(S2-1) [15]
8.a) State and prove Time-reversal, Time-Shifting and scaling properties w.r.to
Z-transform
b) A system has an impulse response h(n) = {1,2,3} and output response
y(n) = {1,1,2,-1,3}. Determine the input sequence x(n). [15]
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