Parseval's identity

The energy of a periodic function is the same in the time and frequency domain.

In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function. The identity asserts the equality of the energy of a periodic signal and the energy of its frequency domain representation. Geometrically, it is a generalized Pythagorean theorem for inner-product spaces.

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