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The spectrum-estimation methods based on the Fourier transform suffer from the major problem of resolution. The methods were developed and are mostly applied for periodic signals under the assumption that only harmonics are present and the periodicity intervals are fixed, while periodicity intervals in the presence of interharmonics are variable and very long. A novel approach to harmonic and interharmonic analysis based on the "subspace" methods is proposed. Min-norm and music harmonic retrieval methods are examples of high-resolution eigenstructure-based methods. Their resolution is theoretically independent of the signal-to-noise ratio (SNR). The Prony method as applied for parameter estimation of signal components was also tested in the paper. Both the high-resolution methods do not show the disadvantages of the traditional tools and allow exact estimation of the interharmonic frequencies. To investigate the methods, several experiments were carried out using simulated signals, current waveforms at the output of an industrial frequency converter, and current waveforms during out-of-step operation of a synchronous generator. For comparison, similar experiments were repeated using the fast Fourier transform (FFT). The comparison proved the superiority of the new methods.