Frequency is an important indicator for the quality of electric power. Accurate spectral decompositions rely much on the correct identification of frequencies of the measured signals. An efficient procedure that includes a high-resolution Prony-based method in conjunction with the downsampling technique for harmonics and interharmonics detection of the measured power signal is proposed in this paper. It is shown that even when two or more closely adjacent spectral lines are present, the proposed method can precisely detect the harmonic and interharmonic components. The performance of the proposed method is validated by testing the simulated and actual measured power signals. Results are compared with those obtained by fast Fourier transform with and without synchronization, IEC subgrouping method, and other commonly used linear prediction approaches adopted in the Prony's method. It shows that the proposed method is more accurate on the detection of harmonics and interharmonics with high resolution.