Use of a sinusoidal series for modeling discrete windowed data as an alternative to interpolation

The use of a sinusoidal series representation as an alternative to interpolation is introduced. The method is applied to both one-dimensional and two-dimensional data. It is noted that the Fourier series can be used here only if the variable of interest has no discontinuities and has the same values at the end boundaries. For situations where this is not the case we introduce the idea of adding to the Fourier series sinusoids at half the fundamental frequency. The procedure is extended to two-dimensional data and applied to terrain modeling where coarse range scanning has been performed and a model of finer resolution is then obtained. Results are shown to be excellent.