## Fourier series & Transform

Example:

- for
, in

- Then,

Parseval’s theorem:

## Fourier transform

- f(x) satisfied
**dirichlet Condition** - f(x) must be periodic, with fundamental period

Q: Can we find F.S, for **integral transform**

Arrangement:

- introduction of F.T.
- Laplace transform (other integral transform

Suppose that

by formula,

(we define

Q: What happens to the above formula when

AKA

Let

The above formula is from the **Fourier inversion theorem 逆傅立叶变换**

**Def:**- F.T. of
: - I.F.T.:

Find the F.T. of f(t)

A:

## The Dirac function

**Def:**The**Dirac**can befunction **loosely**thought of as a function on the real line which is zero everywhere except at the origin, which is infinite.and is also constrained to satisfy the identity:

. Property:

Last Updated on 3 years by Yichen Liu