Question 3 (25 marks) a) Find the z-transform of the following sequences i. {n + 2}u[n] ii. {n^3}u[n] b) Find the inverse z-transform of the following: i. Z^-1 [z|2| sin 3 / z^2 - (2|2| cos 3)z + |2|^2] ii. Z^-1 z(z^2 + 4z + 1) / (z - 1)^4 iii. Z^-1 z(z + 1^4) / (z - 1^3)^3
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Applying the z-transform: $X_1(z) = \sum_{n=0}^{\infty} (n + 2)z^{-n}$ We can split this into two separate sums: $X_1(z) = \sum_{n=0}^{\infty} nz^{-n} + \sum_{n=0}^{\infty} 2z^{-n}$ Now, we can use the known z-transform pairs: $\sum_{n=0}^{\infty} nz^{-n} Show more…
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Question 3 (25 marks) a) Find the z-transform of the following sequences i. {n + 2}u[n] ii. {n^3}u[n] b) Find the inverse z-transform of the following: i. Z^-1 [ z|2|sin 3 / z^2-(2|2|cos 3)z+|2|^2 ] ii. Z^-1 z(z^2+4z+1) / (z-1)^4 iii. Z^-1 z(z+1^4) / (z-1^3)^3
Sri K.
2) Find the Z-transform of a) e^{-3t-7} b) e^{-t}t^2 c) e^{-t}cos2t d) cos(2t+T) e) e^{-2t}cos3t f) 2^nδ(n-2) g) (1/2)^n u(n) h) n^3 3) Find the inverse Z-transform of the following sequence a) z / ((z-1)(z-2)) b) (z^2+2z) / ((z-1)(z-2)(z-3)) c) (z^2-3z) / (z^2-3z+10) d) (z^2(z-1)) / (z^2+1)^2
Adi S.
Find the inverse Z transform for the following function: Hint - it might help to consider F(z)/z.
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