Laplace transform of periodic functions

Let f(t) be periodic with the positive period ( p.  Denote by H(t) the Heaviside step function.  If now


then it follows

g(t)={f(t)for  0<t<p,0   otherwise. (1)

By the parent entry (, the Laplace transformMathworldPlanetmath of g is




Thus we have the rule

{f(t)}=11-e-ps0pe-stf(t)𝑑t  (period p). (2)

On the contrary, if f(t) is antiperiodic with positive antiperiod p, then the function


also has the property (1).  Analogically with the preceding procedure, one may derive the rule

{f(t)}=11+e-ps0pe-stf(t)𝑑t  (antiperiod p). (3)
Title Laplace transform of periodic functions
Canonical name LaplaceTransformOfPeriodicFunctions
Date of creation 2013-03-22 18:58:24
Last modified on 2013-03-22 18:58:24
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Derivation
Classification msc 44A10
Related topic RectificationOfAntiperiodicFunction
Related topic TableOfLaplaceTransforms