Interpolation capability of the periodic radial basis function network

A periodic radial basis function (RBF) network based on the regularisation approach is proposed. The periodic RBF network can eliminate the Gibbs phenomenon observed in the conventional RBF network at the boundary of the data. For the evaluation of the interpolation capability, the frequency response of the periodic RBF network is analysed. It is then theoretically shown that the frequency response is asymptotically equivalent to the ideal sinc interpolation, and that the RBF interpolation is closer to the ideal sinc interpolation than the cubic spline and Lanczos interpolations.