B B4B082 Pages: 4

5. a) The step response of an LTI system is by (1 — ९८ — te~)u(t). For an input x(t), the
output is observed to be (2—3e +e *)u(t). For this observed measurement,

determine the input to the system using laplace transform. (6)

b) State the sampling theorem for low pass signals (2)
c) Determine the Nyquist rate of sampling for the signals
i) x(t) = 2sin 25071 + 30085001 (2)
ii) x(t) = 10 sinc 5001 (3)
d) A signal x(t) = 2 cos 40018 + 6cos 600 mt 15 sampled with a sampling frequency
800Hz. Write the resultant discrete time signal. (2)

6. a) Find the Fourier Transform of following signals x;(t) and x2(t)

(Any relevant property can be applied) (10)
‏ےہ‎

b) A continuous time LTI system is described by the differential equation

d
34 Sy(t) = x(t
۷۷0 + Sy Ct) = x(t)
Determine the response of the system 10 the input x(t) = വ്യ using Fourier
Transform. (5)
PART C
Question 9 is compulsory.

7. a) Evaluate the inverse Z-transform of

X(z) = log lal<|z| (4)

1-7-1

b) Evaluate the DTFT of following signals
i) x(n) =a" sin (20 nu(n) (4)

Page 3 of 4