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We investigate convergence of the rational-trigonometric-polynomial interpolation thatperforms convergence acceleration of the classical trigonometric interpolation by sequentialapplication of polynomial and rational correction functions. Unknown parameters of the ra-tional corrections are determined along the ideas of the Fourier-Pade approximations. Theresultant interpolation we call as Fourier-Pade interpolation and investigate its convergencein the regions away from the endpoints. Comparison with other rational-trigonometric-polynomial interpolations outlines the convergence properties of the Fourier-Pade interpola-tion.