Question

Given the difference equation 4y(n-2)-6y(n-1)+8y(n)=x(n) where the input excitation x(n)=(1/4)n u(n) and the initial conditions are y(0)=1 and y(1) =2​

Answer 1

Answer:

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])

Answer 2

Answer:

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])

Explanation:

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