# Applied Mathematics/Parseval's Theorem

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## Parseval's theorem[edit]

where represents the continuous Fourier transform of *x*(*t*) and *f* represents the frequency component of *x*. The function above is called **Parseval's theorem**.

## Derivation[edit]

Let be the complex conjugation of .

Here, we know that is eqaul to the expansion coefficient of in fourier transforming of .

Hence, the integral of is

Hence