Consider a Linear Time-Invariant (LTI) system with input x(n) and output y(n) related by the following difference equation 3 yln] –yln – 1] +yln – 2] = x[n] a) Determine the Z-transform. b) Propose the impulse response for the following system: i) ii) causal stable iii) neither stable nor causal Find the region of convergence (ROC) of the Z-transform in each of the above cases.

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Consider a Linear Time-Invariant (LTI) system with input x(n) and output y(n) related by the
following difference equation
5
3
y[n] -2y[n-1] + 일n-2] =D x[n]
a) Determine the Z-transform.
b) Propose the impulse response for the following system:
i)
causal
ii)
stable
iii)
neither stable nor causal
Find the region of convergence (ROC) of the Z-transform in each of the above cases.
Transcribed Image Text:Consider a Linear Time-Invariant (LTI) system with input x(n) and output y(n) related by the following difference equation 5 3 y[n] -2y[n-1] + 일n-2] =D x[n] a) Determine the Z-transform. b) Propose the impulse response for the following system: i) causal ii) stable iii) neither stable nor causal Find the region of convergence (ROC) of the Z-transform in each of the above cases.
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