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This paper researches the amplitude modulated Fourier series (AMFS). For a non-stationary signal for which the spectrum is a function of the time, using constant coefficients of Fourier series means the losing local information of the spectrum. The amplitudes of AMFS, which vary as the function of the time, can improve the time-frequency localization for signal analysis. AMFS can also approximate the function in local time domain more accurately. Experiments show that AMFS is a useful tool for time-frequency analysis and function approximating.