R09 - December, 2011 - Regular Examinations - Set - 3.

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
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1.a) Discuss the concept of orthogonality in complex functions and derive the expression for component vector of approximating the function f1(t) over f2(t) in case of complex functions.
b) Derive the expression for Mean square Error in approximating a function f(t) by a set of n orthogonal functions. [15]
2.a) State the necessary and sufficient conditions for the existence of Fourier series representation of a Periodic Signal.
b) Obtain the trigonometric Fourier series for the signal shown in Figure.1. [15]
Figure.1
3.a) State and prove any Four Properties of Fourier Transform.
b) Find the Fourier Transform of
i) f(t) = e-at Cos(bt) ii) f(t) = t cosat. [15]
4.a) Define the terms:
i) Signal Bandwidth ii) System bandwidth
iii) Linear time Variant system iv)Paley-wiener criteria for physical realizability.
b) Test the linearity, causality, time-variance, stability of the system governed by the equation
i) y(n) = ax(n) b ii) y(n) = n cos[x(n)] [15]
5.a) Explain the process of detection of periodic signals by the process of correlation.
b) Define autocorrelation and state its properties. [15]
6. Define Sampling Theorem and discuss the way of performing sampling using Natural sampling technique and compare it with impulse sampling. [15]
7.a) State any four properties of Laplace transform.
b) Find the Laplace transform of the wave form shown in Figure.2.
Figure.2
c) Find the inverse Laplace transform of (S-1) / (S) (S 1). [15]
8.a) Using scaling property determine the Z-transform of an cos?n and find its ROC.
b) Using differentiation property find the Z-transform of x(n) = n2 u(n).
c) Obtain the Z-transform of x(n) = -anu(-n-1) and find its ROC. [15]
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