Size properties of wavelet packets generated using finite filters

  • Morten Nielsen

    University of South Carolina, Columbia, USA


We show that asymptotic estimates for the growth in Lp(r)L^p(\mathbb{r})-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 p2p\gg 2 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 Lp(R)L^p(\mathbb{R}) for p2p\gg 2. Finally, we show that the same type of results are true for the associated periodic wavelet packets in Lp[0,1)L^p[0,1).

Cite this article

Morten Nielsen, Size properties of wavelet packets generated using finite filters. Rev. Mat. Iberoam. 18 (2002), no. 2, pp. 249–265

DOI 10.4171/RMI/318