# Dictionary:Parseval’s theorem

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有两个非周期函数*h*_{1}(*t*)与*h*_{2}(*t*), 其傅里叶变换分别为*H*_{1}(*f*)和 *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.