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With the increase in the use of high-frequency power electronic devices, the harmonics injected into the power grid show a trend of high-frequency development. The continuous rise of the supraharmonic emission level in the distribution network has become one of the power quality problems that needs to be solved urgently in the power grid. In this paper, an algorithm based on the Interpolation of the Self-convolutional Window All-phase Compressive Sampling Matching Pursuit (ISWApCoSaMP) is proposed. Firstly, the self-convolution operation is used for the maximum sidelobe decay (MSD) window, and then the compressed sampling matching pursuit model based on the All-phase is constructed, leading to the All-phase Compressive Sampling Matching Pursuit (ApCoSaMP). Finally, the four-spectrum-line interpolation is combined to utilize spectrum line information to improve the accuracy of signal parameter detection in the frequency domain. The introduced All-phase greatly improves the phase measurement accuracy because the initial phase of the supraharmonic signal is selected for phase estimation. In addition, the self-convolutional window and four-spectrum-line interpolation make full use of the information in the time and frequency domains, thus optimizing the measurement results of amplitude and frequency. The algorithm achieves high accuracy in the measurement results of simulated signals and accurately measures supraharmonics. [ABSTRACT FROM AUTHOR]