6533b7d1fe1ef96bd125d25e
RESEARCH PRODUCT
Non-Dyadic Wavelet Analysis
Dsg PollockIolanda Lo Casciosubject
Band-limited processNon-dyadic mixed radix wavelet analysiSettore SECS-P/05 - EconometriaWaveletdescription
The conventional dyadic multiresolution analysis constructs a succession of frequency intervals in the form of $(\pi/2^j, \pi/2^{j-1});j = 1, 2, \ldots, n$ 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. This paper describes a non-dyadic mixed-radix wavelet analysis which 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.
year | journal | country | edition | language |
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2006-01-01 |