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1.
ESE563 1
Azlin-Fatta-Fad 4a Exercise 2. What is the z-transform of K3 u[k]? ������ ������ ������[������] (−������ ������������ ) ������[������] ������ ������ = 1 ⋅ ������ ������ ������ ∴ ������ ������ = ������ − 1 ������ ������ ������ (−������ ������������ ) [−������ ������������ ] ������−1 ������ ������������ ′ − ������ ������ ′ = >> ������ = ������ ������′ = 1 ������ ������ 2 ������ = ������ − 1 ������′ = 1 ������ ������−1 1 − ������ 1 (−������ ) −������[ } ������������ ������−1 2 ������ −������ (−������ ������������ ) [ ������−1 2 ] ������ ������ −������ (−������ ) [−������ ] ������������ ������������ (������−1)2 ������ ������������ ′ − ������ ������ ′ = >> ������ = −������ ������′ = −1 ������ ������ 2 ������ = (������ − 1)2 ������′ = 2(������ − 1)(1)
2.
ESE563 2
Azlin-Fatta-Fad ������ ������−1 2 −1 − −������ 2 ������−1 (1) −������ −������[ } ������������ ������−1 4 1 ������ ������−1 (−������ 2 +������+2������ 2 ) −������ [ ������������ (������−1)(������−1)3 ������ ������ 2 +������ (−������) [ ] ������������ ������−1 3 ������ ������������ ′ − ������ ������ ′ = >> ������ = ������ 2 + ������ ������′ = 2������ + 1 ������ ������ 2 ������ = (������ − 1)3 ������′ = 3(������ − 1)2(1) ������−1 3 2������+1 − ������ 2 +������ 3 ������−1 2 (1) −������ { } ������−1 6 1 ������−1 2[ ������−1 2������+1)−(������ 2 +������ 3 ] −������ { } ������−1 2 ������−1 4 1 2������ 2 −2������+������−1−3������ 2 −3������ −������ [ ] ������−1 4 ������ 3 +4������ 2 +������ ������−1 4