In order to reconstruct discontinuous signal with the least error by using finite information

the concept of all-phase data processing and the conventional Fourier approximation were combined. By utilizing the coefficients acquired by discrete Fourier transforming the samples of signal and the high harmonic information

all-phase Fourier reconstruction was formed. Theoretical deduction and experimental research show that the waveform reconstructed by all-phase Fourier method has less error than those constructed by conventional continuous Fourier integral approximation and the discrete Fourier reconstruction.