We show that asymptotic estimates for the growth in -norm of a certain subsequence of the basic wavelet packets associated with a finite filter can be obtained in terms of the spectral radius of a subdivision operator associated with the filter. We obtain lower bounds for this growth for using finite dimensional methods. We apply the method to get estimates for the wavelet packets associated with the Daubechies, least asymmetric Daubechies, and Coiflet filters. A consequence of the estimates is that such basis wavelet packets cannot constitute a Schauder basis for for . Finally, we show that the same type of results are true for the associated periodic wavelet packets in .
Cite this article
Morten Nielsen, Size properties of wavelet packets generated using finite filters. Rev. Mat. Iberoam. 18 (2002), no. 2, pp. 249–265DOI 10.4171/RMI/318