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Harmonics and interharmonics adversely affect power grids. The fast Fourier transform (FFT) algorithm is one of the most commonly used methods for harmonic analysis. However, in practical applications, the accuracy of harmonic analysis can be seriously affected by fence effect and spectral leakage, which are undesired characteristics inherent to discrete Fourier transforms. Moreover, when non‐synchronous sampling is carried out, the phase measurement is not accurate enough, and there is a large error in the identification of interharmonics. In order to improve the measurement precision, the method of all‐phase spectrum analysis is used, since it has the characteristics of phase invariance and good spectral leakage suppression. A novel method based on improved Nuttall double‐window all‐phase FFT is proposed by improving the window function and the spectrum correction method for achieving higher precision. Through simulation and experimental verification, the proposed algorithm has proven to perform better than the traditional algorithms both for the detection of harmonics and interharmonics. In addition, the computation burden is not considerably increased when compared to such algorithms, which allows the on‐line use of the proposed algorithm. [ABSTRACT FROM AUTHOR]