超高斯谱函数及其时-频局域化特征

首先在频域定义第一类、第二类超高斯谱函数并推导出其时域解析表达式,然后引用时间算子和频率算子分析两类超高斯谱函数的时间局域化、频域局域化和时-频局域化特征.研究结果表明:时间算子和频率算子对于时-频分析是两个很有用的数学工具;超高斯谱函数的基本性质十分有利于构造规范正交尺度和子波;超高斯谱函数的带宽主要取决于形状因子,时宽主要取决于超高斯谱的阶数,而时-频局域化特征仅与阶数有关.

Super-Gaussian Spectrum Functions and Their Time-Frequency Localization Characteristics

Class one and class two super Gaussian spectrum functions are defined firstly in frequency domain,and then their explicit analytic expressions in time domain are deduced.Time operator and frequency operator are introduced to analyse the time,frequency and time frequency localization characteristics of the aforementioned two new class of functions.Theoretical analysis and results of numerical simulations show that:i)Time operator and frequency operator are very useful mathematical tool for time frequency analysis;ii)The basic properties of super Gaussian spectrum functions are useful in constructing orthonormal and almost orthonormal scaling functions and wavelets;iii)The bandwidth of super Gaussian spectrum functions is decided mainly by their shape factor;the time width of super Gaussian spectrum functions is controlled chiefly their order;time frequency localization characteristics of super Gaussian spectrum functions depend only on their order.