Analysis of Energy Loss-Gain Error in Discrete Fourier Transform

In asynchronous sampling, discrete Fourier transform (DFT) spectrum involves errors. Scholars have done great investigations on the correction techniques of DFT spectrum, but the errors have not been completely eliminated all along. In this paper, spectrums were examined from the principle of conservation of energy. It is unnoticed before that the energy of the digital signal, which is the analysis object of DFT, isn't equal to that of the finite continuous signal truncated by rectangular window. Thus the energy of their spectrums are different according to the Parseval's theorem. The Energy Loss-Gain (ELG) error was introduced to express the energy difference between these two spectrums. The ELG error is zero if the observed continuous signal is truncated in integral multiple of half cycle and it is related to the cycle number and sampling number in one cycle. Analysis show that the ELG error decreases with the increment of these two parameters, which are helpful to the engineering.