Complex wavelet transforms with allpass filters

Complex discrete wavelet transforms (DWT) have significant advantages over real wavelet transforms for certain signal processing problems. Two approaches to the implementation of complex wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having appro...

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Bibliographic Details
Published in:Signal processing 2003-08, Vol.83 (8), p.1689-1706
Main Authors: Fernandes, Felix C.A., Selesnick, Ivan W., van Spaendonck, Rutger L.C., Burrus, C.Sidney
Format: Article
Language:English
Subjects:
Applied sciences
Complex wavelets
Detection, estimation, filtering, equalization, prediction
Dual-tree
Exact sciences and technology
Fractional delay
Information, signal and communications theory
Minimax allpass filters
Non-redundant Hilbert transform
Signal and communications theory
Signal, noise
Telecommunications and information theory
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Summary:Complex discrete wavelet transforms (DWT) have significant advantages over real wavelet transforms for certain signal processing problems. Two approaches to the implementation of complex wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having approximately linear-phase and (fractional) delay. This paper compares the results when different allpass systems are used. In the earlier work, maximally flat delay allpass systems were used. In this paper, it is shown that an allpass system designed according to the minimax criterion yields improvements for the complex DWT.
ISSN:0165-1684
1872-7557
DOI:10.1016/S0165-1684(03)00077-X