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