B4B082 Pages: 4
ii) x(n) = 0.25" u(n+2) (4)
c) Give the Parseval’s theorem for DTFT. Prove it. (4)

sin 02८11

0) Compute the energy of the sequence x(n) = (4)

771
OR

a) A system is described by the difference equation

y(n) = x(n) - x(n - 1) - 130 - 1) + ayn - 2)

Determine the impulse response of the system using fourier transform. Also find the step

response of the system. (8)

b) An LTI system is characterized by the system function given as
3 - 42

سر سس سے سے ‎H(z)‏
‎1-—3.5z-1 + 1.5272‏ 2

Under what conditions the system will be obey causality and stability? (4)
Determine the impulse response of the system such that
i) The system is causal ii) The system is stable

Justify the answers. (8)

. 2) The frequency response of a three point moving average system is given as

H(e/®) = - (1 + cos Q) ९9. Determine the difference equation representation
of the system. (5)
b) Determine the response of the system with impulse response h(n) = (0.5)" u(n) 10
the input signal x(n) = 10 - 5 11 on (5)
c) Find the z-transform and specify ROC
i) x(n) =u(n—2) * ‏00ہ‎ (* stands for convolution) (5)
1) x(n) = —n(Z)"u(-n - 1) (5)
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