# Laplace transforms be converted to fourier transforms?

1. Aug 23, 2009

### monty37

can equations involving laplace transforms be converted to fourier transforms?

2. Aug 23, 2009

### Tom Mattson

Staff Emeritus
Re: transforms

Fourier transforms are special cases of Laplace transforms. In the Laplace transform you typically start with a function $f(t)$ and transform it to a function $F(s)$, where $s$ is a complex variable. For definiteness: $s=\sigma + i\omega$, $\sigma ,\omega\in\mathbb{R}$. Let $\mathcal{F}$ denote Fourier transformation and let $\mathcal{L}$ denote Laplace transformation.

Then:

$$\mathcal{F}[f(t)]=\mathcal{L}[f(t)]|_{\sigma =0}$$

3. Aug 25, 2009

### monty37

Re: transforms

are fourier transforms defined for tan functions as they are defined for sine and cosine
functions?and where do we use these transforms?