Compactly Supported Wavelets Based on Almost Interpolating and Nearly Linear Phase Filters (Coiflets)

New compactly supported wavelets for which both the scaling and wavelet functions have a high number of vanishing moments are presented. Such wavelets are a generalization of the so-called coiflets and they are useful in applications where interpolation and linear phase are of importance. The new approach is to parameterize coiflets by the first moment of the scaling function. By allowing noninteger values for this parameter, the interpolation and linear phase properties of coiflets are optimized. Besides giving a new definition for coiflets, a new system for the filter coefficients is introduced. This system has a minimal set of defining equations and can be solved with algebraic or numerical methods. Examples are given of the various types of coiflets that can be obtained from such systems. The corresponding filter coefficients are listed and their properties are illustrated.  1999