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This letter proposes an analytical method based on 3-D Fourier integral to obtain accurate spectra of both the switching functions and the synthesized terminal quantities of a matrix converter. The challenges associated with the spectral analysis of matrix converter waveforms are twofold. On one hand, the modulation signal contains both the input and output frequencies. Unlike the third-harmonic injection in the modulation functions, the input frequency and the output frequency are typically independent from each other and will not form an integer ratio. On the other hand, it is very common that the switching frequency or the carrier frequency is not rational multiple of either the input frequency or the output frequency. These aforementioned challenges make it a very challenging task to accurately characterize the spectra of matrix converter waveforms through commonly resorted numerical methods such as a fast Fourier transform (FFT). The contribution of the proposed analytical method lies in providing accurate solution to spectral analysis of matrix converters when the FFT approach fails to characterize the spectral performance of matrix converters under typical operating conditions.