Dictionary:Parseval’s theorem

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FIG. F-22. Fourier transform theorems.

(par’ s∂ v∂lz) For two aperiodic functions h1(t) and h2(t) with respective Fourier transforms H1(f) and H2(f),

Thus the zero-lag value of the crosscorrelation File:Fgr.gif12(0), the two values on the left, equals the integral of the cross-product spectrum and the cross-power-spectral amplitude at zero frequency Φ12(0), the two terms on the right. Both equal the cross-energy in the time domain. See Figure F-22. Named for Marc-Antoinne Parseval des Chenes (1755–1836), French mathematician.

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