**The Laplace Transform**

Part 7: Periodic functions

Let us consider a general periodic function *f*(*x*), with period *T*, and its Laplace transform. From the definition of the Laplace transform,

.

Now, dividing up the region of integration into (infinitely many) intervals of length *T*, we get

.

Next, on each integral term, we perform the substitution *u*=*t*–*nT*, which gives us

.

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Tags: Geometric Series, Laplace Transform, Math, Monday Math, Periodic Function

This entry was posted on February 1, 2010 at 12:27 am and is filed under Math/Science. You can follow any responses to this entry through the RSS 2.0 feed.
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March 8, 2010 at 12:43 am |

[…] consider the square wave with period 2π given by . As this is a periodic function, we use our periodic function Laplace transform , where T is the period. For our current function, this gives us: . Possibly related posts: […]