Editing Plancherel theorem (section)

{{Short description|Theorem in harmonic analysis}}
In [[mathematics]], the '''Plancherel theorem''' (sometimes called the '''Parseval–Plancherel identity''') is a result in [[harmonic analysis]], proven by [[Michel Plancherel]] in 1910. It is a generalization of [[Parseval's theorem]]; often used in the fields of science and engineering, proving the [[unitary transformation|unitarity]] of the [[Fourier transform]].

The theorem states that the integral of a function's [[squared modulus]] is equal to the integral of the squared modulus of its [[frequency spectrum]]. That is, if <math>f(x) </math> is a function on the real line, and <math>\widehat{f}(\xi)</math> is its frequency spectrum, then
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|equation = <math>\int_{-\infty}^\infty |f(x)|^2 \, dx = \int_{-\infty}^\infty |\widehat{f}(\xi)|^2  \, d\xi</math>
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