Question

How do you find `F( s ) = \int _ { - \infty } ^ { + \infty } f ( x ) e ^ { - j 2\pi s x } d x`?

Answer 1

That looks like the Fourier Transform of `f(x)`.

In terms of solutions:

• sometimes the actual integration is trivial,

• there exist transform tables for the most common/useful transforms, and

• Fourier Transforms have some useful properties (eg time/frequency shifting, duality) that allow you to move between established transforms without needing to do any real work.

But all you currently have is a definition of the transform:

`ccF {f(x)} = F( s ) = \int _ { - \infty } ^ { + \infty } f ( x ) e ^ { - j 2\pi s x } d x`