Vector-valued wavelets and vector filter banks

Xiang Gen Xia*, Bruce W. Suter

*Corresponding author for this work

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Abstract

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector filter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued wavelets, multiwavelets can be constructed from vector-valued wavelets. We show that certain linear combinations of known scalar-valued wavelets may yield multiwavelets. We then present discrete vector wavelet transforms for discrete-time vector-valued (or blocked) signals, which can be thought of as a family of unitary vector transforms.

Original languageEnglish
Pages (from-to)508-518
Number of pages11
JournalIEEE Transactions on Signal Processing
Volume44
Issue number3
DOIs
Publication statusPublished - 1996
Externally publishedYes

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Xia, X. G., & Suter, B. W. (1996). Vector-valued wavelets and vector filter banks. IEEE Transactions on Signal Processing, 44(3), 508-518. https://doi.org/10.1109/78.489024