Question

1. Determine the response of LTI system having difference equation y(n)-0-6 (n-1) =x(n), n>=o when the input signal is x(n)= (1/2)^n u(n) ​

Answer 1

Answer:

Find the output y(n) when the input x(n) is x(n) = ✓. 1. 2◇ n u(n). 1.4.11 A discrete-time LTI system has impulse response h(n) = 2 ✓. 1. 5◇ n u(n).

Answer 2

For the system to be causal and stable, the poles must lie within the unit

circle. It follows that |a| > 1 must hold.

b)

Y (z)

X(z)

=

10 − 2z

−1

a

2 + 2az−1 + z

−2

Y (z)(a

2 + 2az−1 + z

−2

) = X(z)(10 − 2z

−1

)

a

2

y[n] + 2ay[n − 1] + y[n − 2] = 10x[n] − 2x[n − 1]

y[n] = 1

a

2

(10x[n] − 2x[n − 1] − 2ay[n − 1] − y[n − 2])

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