- #1
redundant6939
- 10
- 0
Find the LT and specify ROC of:
x(t) = e-at, 0 ≤ t ≤ T
= 0, elsewhere
where a > 0
Attempt:
X(s) = - 1/(s+a)*e-(s+a) integrated from 0 to T
=> -1/(s+a)[e-(s+a) + 1]
Converges to X(s) = 1/(s+a) , a ⊂ R, if Re{s} > -a for 0≤t≤T
Elsewhere ROC is empty (LT doesn't exist).
Is this correct?
x(t) = e-at, 0 ≤ t ≤ T
= 0, elsewhere
where a > 0
Attempt:
X(s) = - 1/(s+a)*e-(s+a) integrated from 0 to T
=> -1/(s+a)[e-(s+a) + 1]
Converges to X(s) = 1/(s+a) , a ⊂ R, if Re{s} > -a for 0≤t≤T
Elsewhere ROC is empty (LT doesn't exist).
Is this correct?