Hello,

I want to know what is the different between Laplace transform and Fourier transform?

Can anyone show me? and help me about it?

- Dec 28th 2010, 06:51 PMHamedLaplace transform and Fourier transform what is the different?
Hello,

I want to know what is the different between Laplace transform and Fourier transform?

Can anyone show me? and help me about it? - Dec 28th 2010, 06:58 PMBruno J.
Well, for one, they don't have the same definition. What else do you want to know? You have to be specific.

- Dec 28th 2010, 07:28 PMChris L T521
They have a different kernel. In Laplace, the kernel is $\displaystyle e^{-st}$. In Fourier, the kernel is $\displaystyle e^{-2\pi i x t}$

Also, they are defined over different domains. Laplace is calculated for $\displaystyle t>0$, where as in Fourier, $\displaystyle t\in(-\infty,\infty)$.

As Bruno said, please be more specific in what you're asking. These are just a couple of the differences between these two transforms. - Dec 28th 2010, 11:30 PMHamed
My master told me they are same frequency domain and I said no they are different and Fourier is frequency domain!

What is Laplace domain? - Dec 29th 2010, 01:35 AMCaptainBlack
For an absolutely integrable real function $\displaystyle f(x)$ which is zero for all $\displaystyle x<0$, then $\displaystyle (Ff)(\omega)=(Lf)(i \omega)$ (assuming I have done the algebra right and give or take a multiplicative constant due to how the FT is defined)

CB - Dec 29th 2010, 03:29 AMHamed
Your are right!

But I need show diffrent

In wiki I read this :

Quote:

The Laplace transform is related to the Fourier transform, but whereas the Fourier transform resolves a function or signal into its modes of__vibration__, the Laplace transform resolves a function into its__moments__. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations

- Dec 29th 2010, 09:53 AMCaptainBlack
Exactly what do you not understand in the phrase "the Fourier transform resolves a function or signal into its modes of vibration"?

And the phrase "the Laplace transform resolves a function into its moments" (you can Google for the definition of what the moments of a function are if need be)

Both are of use in differential equations because of the relationship between the FT and LT of a derivative and the function itself, and certain other properties which the two transforms have in common such as the convolution theorems, ...

CB - Dec 29th 2010, 07:55 PMHamed
**vibration**and**moments**I can not find exact defenation! - Dec 29th 2010, 10:51 PMCaptainBlack
The Fourier transform gives a representation of a function in terms of a linear supposition of sinusoids, that it analyses the function/signal into vibrational components.

The Laplace transform is related to the moment generating function, and allows the generation of the moments when they exist (in fact they both do).

CB