11.1 Common laplace transforms

Signals and systems Page 1 / 1

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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