D D5830 Pages: 2
Reg No.: Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIFTH SEMESTER B.TECH DEGREE EXAMINATION, APRIL 2018
Course Code: EE307
Course Name: SIGNALS AND SYSTEMS (EE)

Max. Marks: 100 Duration: 3 Hours
PART A
Answer all questions, each carries 5 marks Marks
1 Check theLinearity and Time-invariance of the system y(t)= t?x(t), where y(t) and ൭
x(t) are the output and input respectively.
2 Define Laplace transform and show that (5)
df(t)
“(के ) = sero) - FO
3 State and prove the following properties of Fourier transform: (5)
i)Time shift ii) Time scaling
4 Find the solution of the difference equation. (5)
y(n + 1) + 2y(n) = n, yo =<
5 Find Z transform of the sequences: (5)
i) x,[n] = {3, —2,0,4,2})ii) x2[n] = a? u(—n - 2)
6 Find inverse Z transform of X(Z) = log ಸ್‌ (5)
7 What is a random signal? Explain with an example. (5)
8 State and prove the discrete Fourier transform property phase shifting. (5)
PART B

Answer any two full questions, each carries 10 marks

9 2) The pole-zero plot of a system is shown in Figure 1. Obtain the differential equation (3)
model of the system.

ध

Figure 1. 7
- | क

0

1۔

-2

x -3

-2 -1 2

0) Obtain the unit step response of the system represented by Figure 1. (No plot 15 (7)
required),

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