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IOLANDA LO CASCIO

Non-Dyadic Wavelet Analysis

  • Authors: Pollock, DSG; Lo Cascio, I
  • Publication year: 2006
  • Type: Capitolo o Saggio (Capitolo o saggio)
  • Key words: Wavelets; Non-dyadic mixed radix wavelet analysis; Band-limited process
  • OA Link: http://hdl.handle.net/10447/47438

Abstract

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.