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11.1 Common laplace transforms

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Lists signal and region of convergence for several Laplace transforms.
Signal Laplace Transform Region of Convergence
δ t 1 All s
δ t T s T All s
u t 1 s s 0
u t 1 s s 0
t u t 1 s 2 s 0
t n u t n s n 1 s 0
t n u t n s n 1 s 0
λ t u t 1 s λ s λ
λ t u t 1 s λ s λ
t λ t u t 1 s λ 2 s λ
t n λ t u t n s λ n 1 s λ
t n λ t u t n s λ n 1 s λ
b t u t s s 2 b 2 s 0
b t u t b s 2 b 2 s 0
a t b t u t s a s a 2 b 2 s a
a t b t u t b s a 2 b 2 s a
t n δ t s n All s
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Source:  OpenStax, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15
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