Reconstruct discontinuous signal by all-phase Fourier technique
Yuqing He, Xiangdong Huang
Abstract
Yuqing He, Xiangdong Huang
Abstract
In order to reconstruct discontinuous signal with the least error by using finite information, this paper combines the concept of all-phase data processing and the conventional Fourier approximation. By utilizing the coefficients acquired by discrete Fourier transforming the samples of signal and the high harmonic information, all-phase Fourier reconstruction is 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 approximation.
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In order to reconstruct discontinuous signal with the least error by using finite information, this paper combines the concept of all-phase data processing and the conventional Fourier approximation. By utilizing the coefficients acquired by discrete Fourier transforming the samples of signal and the high harmonic information, all-phase Fourier reconstruction is 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 approximation.
Key concepts: Fourier transform, Discrete Fourier series, Fourier analysis, Phase correlation, Discrete-time Fourier transform, Fourier series, Discrete Fourier transform (general), Harmonic analysis