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.

Pollock, D., Lo Cascio, I. (2006). Non-Dyadic Wavelet Analysis. In Kontoghiorghes E.J., Gatu C.. (a cura di), Optimisation, Econometric and Financial Analysis. (pp. 169-204). Springer.

Non-Dyadic Wavelet Analysis

LO CASCIO, Iolanda
2006-01-01

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.
2006
Pollock, D., Lo Cascio, I. (2006). Non-Dyadic Wavelet Analysis. In Kontoghiorghes E.J., Gatu C.. (a cura di), Optimisation, Econometric and Financial Analysis. (pp. 169-204). Springer.
File in questo prodotto:
File Dimensione Formato  
NONDWAVE.pdf

Solo gestori archvio

Dimensione 274.92 kB
Formato Adobe PDF
274.92 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/47438
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 14
social impact