fourier and Laplace

[Gibson486]

Correct me if I am wrong, but isn't the fourier transform just the laplace transform extended to the whole time axis with s = jw?

If this is true, then how come the LaPlace transform of sin(x) differs from the Fourier transform of sin(x) (it's all delta funtions!)?

 

[chuckywang]

The Laplace transform of sin(t) is 1/(1+s^2). However, from the definition of the Laplace transform, the integral goes from 0 to infinity, whereas the integral in the Fourier Transform goes from -infinity to infinity.

 

[Gibson486]

Originally posted by: chuckywang
The Laplace transform of sin(t) is 1/(1+s^2). However, from the definition of the Laplace transform, the integral goes from 0 to infinity, whereas the integral in the Fourier Transform goes from -infinity to infinity.

yeah, I just got that just now. I was slaving over thsi last night and it never occured to me to just try from scratch and use different integration intervals.