A stability criterion for biorthogonal wavelet bases and their related subband coding scheme. (English) Zbl 0784.42022

It is shown that in the consideration of bi-orthogonal (and non- orthogonal) wavelets, a pair of dual filters does not necessarily lead to a pair of stable bi-orthogonal wavelet bases. The objective of this paper is to derive a stability criterion in terms of the action under a so- called transition operator and its dual. The criterion is that the spectra of both operators lie inside the unit circle.


42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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