Calculate the Z transform of the sequences 1) (−15)k 2) cos⁡kπ 3) 3k

Turnseeuw

Turnseeuw

Answered

2022-01-25

Calculate the Z transform of the sequences
1) (15)k
2) coskπ
3) 3k

Answer & Explanation

Lily Thornton

Lily Thornton

Expert

2022-01-26Added 19 answers

We have the sequence
1) (15)k
x[k]=(15)k
Formula for z-transform is
Z(x[k])=k=0(x[k])zk
Thus,
Z(x[k])=k=0(15)kzk
Z(x[k])=k=0(15z)k=115z+1(5z)2
Above series is geometric series
Thus, Z(x[k])=11(15z)
Z(x[k])=5z5z+1

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