A wavelet “time-shift-detail” decomposition

N. Levan and C.S. Kubrusly

Mathematics and Computers in Simulation (MATCOM), 2003, vol. 63, issue 2, 73-78

Abstract: We show that, with respect to an orthonormal wavelet ψ(·)∈L2(R) any f(·)∈L2(R) is, on the one hand, the sum of its “layers of details” over all time-shifts, and on the other hand, the sum of its layers of details over all scales. The latter is well known and is a consequence of a wandering subspace decomposition of L2(R) which, in turn, resulted from a wavelet multiresolution analysis (MRA). The former has not been discussed before. We show that it is a consequence of a decomposition of L2(R) in terms of reducing subspaces of the dilation-by-2 shift operator.

Keywords: Wavelet; Scale and time-shift-details; Shift-wandering subspace decomposition; Shift reducing subspaces decomposition (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:63:y:2003:i:2:p:73-78

DOI: 10.1016/S0378-4754(03)00037-5

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