Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 59, Issue 8, Pages 3560-3575Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2011.2143711
Keywords
Constant-Q transform; filter bank; Q-factor; wavelet transform
Categories
Funding
- NSF [CCF-1018020]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1018020] Funding Source: National Science Foundation
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This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. Two forms of the transform are presented. The first form is defined for discrete-time signals defined on all of. The second form is defined for discrete-time signals of finite-length and can be implemented efficiently with FFTs. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e.g., three to four times overcomplete) being sufficient for the analysis/synthesis functions to be well localized.
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