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 equal to the expansion coefficient of in fourier transforming of .
Hence, the integral of is
Hence