On the Correlation Structure of Multiplicity M Scaling Functions and Wavelets
Gopinath, Ramesh A.
Odegard, Jan E.
Burrus, C. Sidney
In this paper we study the auto-correlation and cross-correlation structure of the scaling and wavelet functions associated with compactly supported orthonormal wavelet basis. These correlation structures play an important role in both wavelet-based interpolation and in answering the question of existence of scale-limited signals. Our investigations into their nature, gives us a fairly complete account of all the zeros of the correlation functions and also give efficient algorithms for their computation. An interesting fact that arises from the analysis is that all the correlations possible have infinitely many zeros in their support.