|
Table
1. Table of Basic Laplace Transforms
|
Function |
f(t) |
F(s) |
|
Unit
Impulse |
δ(t) |
1 |
|
Ideal
Delay |
δ(t-τ) |
e-τs |
|
Unit
Step |
u(t)
or 1 |
1 / s |
|
Delayed Unit Step |
u(t-τ) |
(e-τs)
/ s |
|
nth
power |
(tn/n!)u(t) |
1 / sn+1 |
|
ramp |
t |
1 / s2 |
|
nth
power with frequency shift |
(tn/n!)e-at |
1 /
(s+a)n+1 |
|
- |
te-at |
1 /
(s+a)2 |
|
exponential decay |
e-at |
1 / (s+a) |
|
exponential approach |
(1-e-at) |
a /
s(s+a) |
|
sine |
sin(ωt) |
ω
/ (s2+ω2) |
|
cosine |
cos(ωt)
|
s
/ (s2+ω2) |
|
hyperbolic sine |
sinh(αt) |
α
/ (s2-α2) |
|
hyperbolic cosine |
cosh(αt)
|
s
/ (s2-α2) |
|
natural logarithm |
ln(t/to) |
-to/s
(ln(tos+γ) |
|
- |
1/(sqrt(πt)) |
1/sqrt(s) |
See Also:
Laplace Transforms;
Math Used
in ECE
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