Frequency domain analysis based RBF networks and their applications to function approximations

Time-domain analysis and frequency-domain analysis are two angles of view for us to study and survey a continuous function. We observe the function approximation problems from the frequency domain. We consider that a single-frequency sine function can be approximated by two Gaussian kernels in one period. According to that, we present that the first maximum amplitudes as well as their frequencies and initial phases can be used to determine the initial number, centers and widths of radial basis function (RBF) kernels. After the initial structure of an RBF network is determined like that, a small number of RBF kernels can be added in order to further improve the local approximation accuracy. The above viewpoint is verified by two approximation examples.