Signals and Systems - Engineering
Q1: The ROC of sequence x[n] = (0.8)n ∪[n] + (0.4)n ∪[n]A |z| > 0.8
B |z| > 0.4
C 0.4 < |z| < 0.8
D |z| < 0.8
ANS:A - |z| > 0.8
ROC ⇒ 1 - 0.8 z-1 < 0 1 - 0.4 z-1
⇒ 1 > 0.8 z-1 ⇒ z > 0.4
or z > 0.8
By combining both condition
ROC because z > 0.4
If you consider z > 0.8 then ROC between the limit 0 to 0.4 excluded.
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ROC ⇒ 1 - 0.8 z-1 < 0 1 - 0.4 z-1
⇒ 1 > 0.8 z-1 ⇒ z > 0.4
or z > 0.8
By combining both condition
ROC because z > 0.4
If you consider z > 0.8 then ROC between the limit 0 to 0.4 excluded.