# Fourier transform

From Class Wiki

An initially identity that is useful:

Suppose that we have some function, say , that is nonperiodic and finite in duration.

This means that for some

Now let's make a periodic function by repeating with a fundamental period .
Note that

The Fourier Series representation of is

where

and

can now be rewritten as

From our initial identity then, we can write as

and
becomes