D 06000EE307122001 Pages: 3

Reg No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
Fifth Semester B.Tech Degree (S,FE) Examination January 2022 (2015 Scheme)

Course Code: EE307
Course Name: SIGNAL AND SYSTEMS

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all questions, each carries 5 marks. Marks
1 Check whether the system y(t) = x (5) is dynamic, linear and time invariant (5)
2 Find the Laplace transform of the function x(t) = V2cos(3t + 45°)u(t). Also (5)
specify the ROC.
3 State and prove the Frequency shifting and Convolution properties of Fourier (5)
Transform.
4 State and prove sampling theorem. (5)
5 State and prove the scaling and time shifting properties of z-transform (5)
6 Find the z-transform of x[n] = 3a@"u[—n]. Indicate ROC, poles and zeros inz- (5)
plane.
7 Explain any five types of non-linear systems. (5)
8 State any 5 properties of Discrete Fourier series. (5)
PART 13
Answer any two full questions, each carries 10 marks.
9 t+2,-21,-1
Consider the signal x(t) = —t4+21
0, elsewhere

a) Write 8 mathematical equation for y(t) = x(—2t — 3).and sketch y(t). (6)
b) Find the total energy of y(t). (4)
10 a) Define signum function. (2)
b) Find the convolution of x(t) and x2(t) given x;(t) 5९ u(t) and x2(t) = e“'u(t). (3)
c) Determine the initial and final values for the given Laplace transform. (5)
5s+4
2७) 7 24+3542

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