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-1z > 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.