  We compare frameworks of nonstationary nonperiodic wavelets and periodic
wavelets. We construct one system from another using periodization. There are
infinitely many nonstationary systems corresponding to the same periodic
wavelet. Under mild conditions on periodic scaling functions, among these
nonstationary wavelet systems, we find a system such that its time-frequency
localization is adjusted with an angular-frequency localization of an initial
periodic wavelet system. Namely, we get the following equality $ \lim_{j\to
\infty} UC_B(\psi^P_j) = \lim_{j\to \infty}UC_H(\psi^N_j), $ where $UC_B$ and
$UC_H$ are the Breitenberger and the Heisenberg uncertainty constants,
$\psi^P_j \in L_2(\mathbb{T})$ and $\psi^N_j\in L_2(\mathbb{R})$ are periodic
and nonstationary wavelet functions respectively.
