Trigonometric polynomial interpolation of periodic functions with period 2; on equidistant points in the interval [0,2;) is a well-known effective approximation tool. A standard numerical procedure implementing this method is based on doubling the number of interpolation points at each step, so that the effective FFT technique is applicable. In this paper, the authors call a set quasi-equidistant point set, when it is the union of equidistant point sets with same size but with mutually different phases. They propose a fast algorithm for trigonometric polynomial interpolation on quasi-equidistant sample points for real periodic functions. The present algorithm is a generalization of real FFT, but still needs O(nlogn) arithmetic operations, where n is a number of interpolation points. With the quasi-equidistant point set and the algorithm for the interpolation on them, an efficient scheme for automatic function approximation can be constructed, in which increasing rate of the number of interpolation points is less than 2 and arbitrary close to 1. [In Japanese.]
