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