School of Economics and Finance

No. 529: Orthogonality Conditions for Non-Dyadic Wavelet Analysis

Stephen Pollock , Queen Mary, University of London
Iolanda Lo Cascio , Queen Mary, University of London

May 1, 2005

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The conventional dyadic multiresolution analysis constructs a succession of frequency intervals in the form of (π / 2 j, π / 2 j - 1); j = 1, 2, . . . , n of which the bandwidths are halved repeatedly in the descent from high frequencies to low frequencies. Whereas this scheme provides an excellent framework for encoding and transmitting signals with a high degree of data compression, it is less appropriate to the purposes of statistical data analysis. A non-dyadic mixed-radix wavelet analysis is described that allows the wave bands to be defined more flexibly than in the case of a conventional dyadic analysis. The wavelets that form the basis vectors for the wave bands are derived from the Fourier transforms of a variety of functions that specify the frequency responses of the filters corresponding to the sequences of wavelet coefficients.

J.E.L classification codes: C22

Keywords:Wavelets, Non-dyadic analysis, Fourier analysis