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R5986 Pages: 2

a continuous time linear time invariant system.

PARTC
Answer any two full questions, each carries 10 marks.

a) Find the exponential Fourier series of the waveform shown in figure. Also plot (7) the
magnitude spectrum with n=0,1,2,3,4 and 5.

f(t)

b) State and prove the time differentiation property of continuous time Fourier (3)
transform (CTFT).

State and prove sampling theorem. Also, explain aliasing. (10)

a) Find the frequency response for the following linear time invariant system and (5) hence
find the impulse response. dy(t) 0 2y( ) 0 x t( ). Also find the output y(t) if the input is
൫00 eu ‏)سا‎ )

dt

b) Find the linear convolution y 11 | 0 x ೧| JUh ‏اص‎ J if ೬[೧1101(111 11) ‏)لا‎ 9 [1(111)
(5)

and 111] 2 (1 1111) [11 ) 2 m0 Onl).

PART D 4
Answer any two full questions, each carries 10 marks.
3 ம்‌
a) Find Z-transform and ROC of x[n]Uu(0 [1 On 1) ‏لا‎ 211 प्र1( ) (6) b) State
and prove the initial value theorem of Z-transforms. (4)
1.
a) A causal discrete time system is described by y n[ ‏لاز‎ y ‏]م‎ [11] y 1[ 1 [12] ‏]ضع‎ |
(7)

. Find the frequency response and impulse response.

b) Find the discrete time Fourier series (DTFS) of ൩1 1,010. (3)
a) A causal 1.11 = system is described by the difference
equation (5)

೫1113 ‏نز‎ 1[ 0 11] 2 [४101] . Find the transfer function and impulse response of
the system.

b) Classify the various physical non-linearities in systems. (5)