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Orthogonality Conditions for Non-Dyadic Wavelet Analysis

  • Stephen Pollock

    (Queen Mary, University of London)

  • Iolanda Lo Cascio

    (Queen Mary, University of London)

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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.

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    File URL: http://www.econ.qmul.ac.uk/papers/doc/wp529.pdf
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    Paper provided by Queen Mary University of London, School of Economics and Finance in its series Working Papers with number 529.

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    Date of creation: May 2005
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    Handle: RePEc:qmw:qmwecw:wp529
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    1. Stephen Pollock, 2000. "Circulant Matrices and Time-series Analysis," Working Papers 422, Queen Mary University of London, School of Economics and Finance.
    2. Nason, G.P. & von Sachs, R., 1999. "Wavelets in Time Series Analysis," Papers 9901, Catholique de Louvain - Institut de statistique.
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