Local reproducible smoothing without shrinkage

A simple local smoothing filter for curves or surfaces, combining the advantages of Gaussian smoothing and Fourier curve description, is defined. Unlike Gaussian filters, the filter described has no shrinkage problem. Repeated application of the filter does not yield a curve or surface smaller than the original, but simply reproduces the approximate result that would have been obtained by a single application at the largest scale. Unlike Fourier description, the filter is local in space. The wavelet transform of Y. Meyer (1989) is shown to have these properties