---
# System prepended metadata

title: Parseval’s Identity
tags: [工程數學]

---

# Parseval’s Identity
###### tags: `工程數學`
## Parseval's Identity
$$\frac {1}{L} \int_{-L}^L{f^2(x)}dx=\frac{a_0^2}{2}+\sum_{n=1}^\infty{(a_n^2+b_n^2)}$$
## Bessel's Inequality
$$\frac {1}{L} \int_{-L}^L{f^2(x)}dx \geq \frac{a_0^2}{2}+\sum_{n=1}^M{(a_n^2+b_n^2)}$$

$$if\ M \rightarrow \infty,\\
Bessel's\ Identity\ becomes\ Parseval's\ Identity$$

