Generalized symmetric interpolating wavelets

Abstract

A new class of biorthogonal wavelets-interpolating distributed approximating functional (DAF) wavelets are proposed as a powerful basis for scale-space functional analysis and approximation. The important advantage is that these wavelets can be designed with infinite smoothness in both time and frequency spaces, and have as well symmetric interpolating characteristics. Boundary adaptive wavelets can be implemented conveniently by simply shifting the window envelope. As examples, generalized Lagrange wavelets and generalized Sinc wavelets are presented and discussed in detail. Efficient applications in computational science and engineering are explored.