Functional Representation, Approximation, Bases and Wavelets

Abstract

After stressing the importance of analyzing the various basis spaces, the exposition evaluates the alternative bases available to wavelet researchers. The next step is to demonstrate the impact of choice of basis for the representation or projection of the regressand. The similarity of formulating a basis is explored across a variety of alternative representations. This development is followed by a very brief overview of some articles using wavelet tools. The comparative advantage of wavelets relative to the alternatives considered is stressed.