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Find Fourier Transform of signal x(t) = te“u(t).
OR
State and prove sampling theorem for low pass signals.
dy(t)
dt
transform, find the output y(t) given x(t) =e“‘u(t).

A signal is given by x(t) = 2Cos(400z1) + 6Cos(6402t) What is the minimum
sampling frequency required to avoid aliasing? If the signal is ideally sampled with
sampling frequency of 500 Hz, what are the frequency components present at the
output?

State and prove time-shifting property of Laplace transform.

Find inverse Laplace transform of നം. - - ROC
(s +1)(s -1)(s +2)

A continuous time LTI system is described by + 2 y(t) = x(t). Using Fourier

- 1 < २९५) < |

For a continuous time LTI system, input x(t)and (1) ೩೯೮ related by
ഗാഗ, dy)
dt dt

that the system is causal.

—2y(t) = x(t). Find system function H(s). Determine h(t) given

PART C
Question 9 is compulsory. Answer question 7 or 8
Write down properties of ROC for Z transform
x[n] is a discrete time periodic square wave with period N and amplitude 1. Non-
zero samples extends from —N; to +N. Find the Fourier coefficients.
Find inverse z-transform of X(z) using power series expansion technique.
2
X(z)= 222-3241 [೭ 1
OR
Determine the discrete Fourier series representation for the sequence

7 ⋅
೫11] 608 7೫ and pot the magnitude and phase response.

⋅ ⋅ ⋅⋅ 1
A discrete time LTI system is given by y[n]— त 171 - 1| = x[n] + ‏اد‎ - 1].
Determine frequency response and impulse response of the system.
Explain the relation between DTFT and z-transform. Explain whether DTFT can
be obtained from z-transform for (i) x[n]=a"u[n] (01) x[n]=u[n]
State and prove convolution property of DTFT.

1, |1|5 ಗಿ] Find Fourier T
ind Fourier Transform

Given x[n]=
[1] 1८ |n|>N,

The step response of a discrete time LTI system is given by s[n]=a"u[n];

0 < > 1, Find impulse response 1/11) of the system using z-transform.

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