Orthogonality Conditions for Non-Dyadic Wavelet Analysis
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.
|Date of creation:||May 2005|
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- Nason, G.P. & von Sachs, R., 1999. "Wavelets in Time Series Analysis," Papers 9901, Catholique de Louvain - Institut de statistique.
- Stephen Pollock, 2000. "Circulant Matrices and Time-series Analysis," Working Papers 422, Queen Mary University of London, School of Economics and Finance.
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