Applied Mathematics/Parseval's Theorem

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Parseval's theorem[edit | edit source]

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 | edit source]

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