论文标题
新型的特殊仿射小波变换和相关的不确定性不平等
Novel Special Affine Wavelet Transform and Associated Uncertainity Inequalities
论文作者
论文摘要
{.2in} {\ small {\ bf Abstract。}由于额外的自由度，特殊的仿射傅立叶变换（SAFT）在短时间内实现了可观的状态，并且在信号处理，图像处理，图像处理，采样理论，量子力学的领域具有多功能的适用性。但是，由于其全球内核，SAFT无法获取非传输信号的本地信息。为了克服这一点，我们在本文中介绍了新型特殊仿射小波变换（NSAWT）的概念，并将关键的谐波分析结果扩展到类似于小波变换的nsawt。我们首先建立了一些基本属性，包括Moyal的原理，反转公式和范围定理。某些海森堡类型的不平等和皮特的不平等是针对SAFT的，因此，海森堡不确定原则是针对NSAWT的。
{.2in} {\small {\bf Abstract.} Due to the extra degrees of freedom, special affine Fourier transform (SAFT) has achieved a respectable status within a short span and got versatile applicability in the areas of signal processing, image processing,sampling theory, quantum mechanics. However, due to its global kernel, SAFT fails to obtain local information of non-transient signals. To overcome this, we in this paper introduce the concept of novel special affine wavelet transform (NSAWT) and extend key harmonic analysis results to NSAWT analogous to those for the wavelet transform. We first establish some fundamental properties including Moyal's principle, Inversion formula and the range theorem. Some Heisenberg type inequalities and Pitt's inequality are established for SAFT and consequently Heisenberg uncertainity principle is derived for NSAWT.
