Fourier transform ↩

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created: 2021-12-03 00:27:59
modified: 2022-01-10 04:13:02

Let

be a continuous function

with at most finitely many discontinuities of the first kind (i.e.

and

exist) and

Then the Fourier transform of :

exists, and the inverse Fourier transform is:

Note that the inverse transformed will be at the original discontinuities.

Properties

Linearity:
When using prefactors in both the transform and its inverse, then it is a unitary linear operator on the space of square-integrable functions

There are several conventions for the Fourier transform, the one shown is just one of them