# Dictionary:Parseval’s theorem

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(par’ s∂ v∂lz) For two aperiodic functions *h*_{1}(*t*) and *h*_{2}(*t*) with respective Fourier transforms *H*_{1}(*f*) and *H*_{2}(*f*),

Thus the zero-lag value of the crosscorrelation _{12}(0), the two values on the left, equals the integral of the cross-product spectrum and the cross-power-spectral amplitude at zero frequency Φ_{12}(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.