-transform of any discrete -time signal can be defined using expression below, X(Z) = x[n]z-, a) By using above Z-transform expression, derive and prove that both discrete-time signal below produces similar X(Z) expression. x, [n] = a"u[n] x2[n] = -a"u[-n – 1] b) Instead of having the same XZ) expression, prove that, both discrete-time signals having different ROC. =) If the x,[n] is used as an input of a system with value of a set to - The system produces an output that express as v[n] = 3(-1)" u[n]+(½) u[n], analyze the impulse response of the system, h[n]. (Hint: you may use Z-transform table in the solution).

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QUESTION 4
Z-transform of any discrete -time signal can be defined using expression below,
+00
X(Z) = > x[n]z-",
(a) Byusing above Z-transfom expression, derive and prove that both discrete-time signal
below produces similar X(Z) expression.
x,[n] = a"u[n]
xz[n] = -a"u[-n – 1]
(b)
Instead of having the same X(Z) expression, prove that, both discrete-time signals
having different ROC.
(c)
If the x,[n] is used as an input of a system with value of a set to
The system
produces an output that express as y[n]= 3(-1)" z[n]+(½) u[n], analyze the
impulse response of the system, h[n]. (Hint: you may use Z-transform table in the
solution).
Transcribed Image Text:QUESTION 4 Z-transform of any discrete -time signal can be defined using expression below, +00 X(Z) = > x[n]z-", (a) Byusing above Z-transfom expression, derive and prove that both discrete-time signal below produces similar X(Z) expression. x,[n] = a"u[n] xz[n] = -a"u[-n – 1] (b) Instead of having the same X(Z) expression, prove that, both discrete-time signals having different ROC. (c) If the x,[n] is used as an input of a system with value of a set to The system produces an output that express as y[n]= 3(-1)" z[n]+(½) u[n], analyze the impulse response of the system, h[n]. (Hint: you may use Z-transform table in the solution).
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