Non-Dyadic Wavelet Analysis

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.