Laplace Transform of Period Square Wave Function

**Blink** · February 28th 2010, 10:30 AM

I'm having trouble setting up my equation.

Square wave with period T = 2a.
f(t) = 2, 0<t<a
f(t) = 0, a<t<2a

Take the Laplace Transform of f(t).

What I got:

F(s) = (∫2exp(-st)dt [0,a]) / [1 - exp(-2as)]

The square brackets [0,a] are the limits of the definite integral.

Thanks guys.

**chisigma** · February 28th 2010, 12:54 PM

If $f(t)$ has period T, then its Laplace transform is...

$F(s)= \mathcal{L} \{f(t)\}= \frac{\int_{0}^{T} e^{-st}\cdot f(t)\cdot dt}{1-e^{-sT}}$ (1)

In Your case is $T=2a$ and the integral in (1) is...

$\int_{0}^{a} 2\cdot e^{-st}\cdot dt$ (2)

... that is easy to solve...

Kind regards

$\chi$ $\sigma$

**Blink** · February 28th 2010, 01:25 PM

Perfect, thank you very much, good to know I was on the right track!

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