关键词: Shannon抽样定理, 小波抽样, 非带限信号, 三次样条, 插值法

Abstract: Several interpolation methods and their applications are focused on on one and two dimension fields.There are six interpolation methods:Shannon,cubic spline,cubic convolution,linear,FFT and cubic spline wavelet interpolations.The last one is based on wavelet sampling without frequency bandlimits.Two one-dimensional signals,i.e.,Shannon interpolation basis function and single pulse,are interpolated by the six methods.It is indicated that the cubic spline is the best interpolation for the frequency-bounded signal(Shannon basis), while the cubic convolution interpolation is the most accurate one among them for the single pulse signal.;Numerical interpolations are carried out for three reanalysis data sets produced by NCEP,National Center for Environmnet Prediction of the United States.Numerical results show that the cubic spline wavelet interpolation is of the highest accuracy for the monthly rainfall field,where the cubic spline interpolation is the best one for the monthly geopotential height field and the sea surface pressure field.The linear and the cubic spline wavelet interpolations are combined to avoid the negative rainfall produced by almost all the interpolations except for the linear one.This method can raise the rainfall interpolation accuracy too.One problem left is that the wavelet interpolation could produce"quot;Gibbs phenomena" by the boundary although it is smaller and more localized than Shannon interpolation.This difficulty remains to solve.

Key words: wavelet sampling, spline, interpolation, meteorology