b)

a)

b)

0)

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b)

0)

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b)

0)

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0)

a)

b)

00000307112103

Obtain the response y(t) from an ideal low pass filter if a rectangular pulse x(t)
is transmitted through it, where x(t) = 08 ١١ < (2)

0, otherwise
State and prove the Parseval’s relation and convolution property of Discrete time
Fourier series.
Obtain the Fourier transform of the signal x(t) = te~ u(t) using an appropriate
property.
Find the Continuous Time Fourier Series coefficients of the signal x(t) = cos4t +
sin6t.
Give the conditions for distortionless transmission through an LTI systems
Find the discrete time Fourier transform of the signal x[n] = -a"u[-n-1], if a is

real and |a| > 1.

∙ | 1
T. 7 01 1८0} ‏ہے‎ _ 7

A DT- LTI system is represented by H(e ) = ന്ന പി

Find the difference equation representing the input-output relation of the system.

PART C
Answer any two full questions, each carries 20 marks.
A causal DT-LTI system is described by y[n] - 221१ - 1] + 521 - 2] =
2 [11], where x[n] and y[n] are input and output of the system. Determine the
system function H(z), impulse response and step response .

Check whether the system described in 7a. is stable. Also find the response
⋅ ⋅ 1

corresponding to an input x[n] = (727 णण.

Derive the relation between Z-Transform and Fourier transform

Gi 1 ⋅ ⋅ ⋅
iven X(s) = 3 <**_ ‏و‎ the Laplace transform using the properties of

+3s+4
Laplace transform .(1) yi(t)=x(2t) (01)920) = ह x(t) (111) y3(t)=x(t) *x(t)
Find the initial and final values of the signal with Laplace transform
5 +4
52+ 36+ 5
Find the Laplace transform and plot ROC of the signal x(t) = ௦082 u(t)

X(s) =

2s+4
524 4543

Find the inverse Laplace transform of X(s) = for the following 3

ROCs (1) Re(s) > -1 (ii) Re(s) > -3 (111) -3 < Re(s) > -1.
Give the properties of ROC of Z-Transform

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(8)