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11013 Pages: 3

An LTI system is described by the following input-output relation

y(n) ~ + - 1) + 39" - 2) = x(n) - 3:00 1).

Determine the impulse response of the system with specified ROCs of H(z) for the
conditions:

(i) System is stable (ii) System is causal

Find the discrete time Fourier series coefficients of the signal x(n) =5 +

sin (=) + cos (=) Plot the magnitude and phase spectrum.

1

Find all possible time domain signals for the Z- transform X(z) = ‏جس‎ അ *
6 6

n
A stable and causal LTI system produces an output y(n) =n 8 u(n), for the

⋅⋅ 4\" ⋅ ⋅ Time Fouri
excitation x(n) = 6 u(n). Using Discrete Time Fourier transform,

(i) Determine the Frequency response of the system.

(ii) Derive the difference equation relating the input and output.

Using Z- transform, determine the output of an LTI system with impulse response
h(n) = {1, 2, -1,0,3) for the input x(n) = {1, 2, —1}.

⋅ ⋅ ‏ہے‎ F ⋅ ↥∏⋅ 7
Determine the Discrete Time Fourier transform of x(n) = 6 sin (=) u(n).

n
4
Compute the Z-transform and ROC of the signal x(n) = (६) "൧൭ — 2™u(—n-1).
Plot the pole-zero pattern.

Mathematically explain how DTFT is related with Z- transform.

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