Interpolation capability of the periodic radial basis function

A periodic radial basis function (RBF) network is proposed based on the regularization approach. The periodic RBF network can interpolate discrete data more efficiently than the conventional one since the coefficients of the network can be computed by using the fast Fourier transform (FFT). For the evaluation of the interpolation capability, the frequency response of the periodic RBF network is analyzed. It is then shown that the frequency response is asymptotically equivalent to the ideal sine interpolation, and that the periodic RBF network is closer to the ideal sine interpolation than the cubic spline and Lanczos interpolations