关于非平稳小波与周期小波的一种联系
On a connection between nonstationary and periodic wavelets
摘要：
我们比较了非平稳非周期小波和周期小波的框架。我们用分期法从一个系统到另一个系统来构造。存在无穷多个对应于同一周期小波的非平稳系统。在周期尺度函数的适当条件下，在这些非平稳小波系统中，我们发现了一个系统，使得它的时频局部化是由初始周期小波系统的角频局部化来调整的。即，我们得到如下等式$ \lim_{j\to \infty} UC_B(ψ^P_j) = \lim_{j\to \infty}UC_H(ψ^N_j), $其中$UC_B$和$UC_H$分别是Breitenberger和Heisenberg测不准常数，$ψ^P_j \in L_2(\mathbb{T})$和$ψ^N_j\in L_2(\mathbb{R})$分别是周期非平稳小波函数.
英文摘要：
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(ψ^P_j) = \lim_{j\to \infty}UC_H(ψ^N_j), $ where $UC_B$ and $UC_H$ are the Breitenberger and the Heisenberg uncertainty constants, $ψ^P_j \in L_2(\mathbb{T})$ and $ψ^N_j\in L_2(\mathbb{R})$ are periodic and nonstationary wavelet functions respectively.
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