摘要
从子波分析的基函数 (即母波 )构造条件入手 ,提出本文研究目的 .文中首先讨论子波分析数值计算稳定性一般问题 ,引进稳定度概念来刻画母波数值反演的稳定程度 ;接着研究一类品质因素可控的复解析母波———Y -母波的稳定度 ;最后分析Y -母波的正交条件 .理论分析和数值计算结果表明 :母波的稳定度与其频率选择性是一对矛盾 ,但选择适当的尺度伸缩因子可以适当缓解这一矛盾 ;由于品质因素的限制 ,二进Y -母波的高稳定度区域是十分狭窄的 ;对于 (复 )Y -母波 ,不存在正交的整数平移基 ,仅有Y -母波的实部 (即实Y -母波 )存在正交的整数平移基 .
Starting with the construction conditions of basic wavelet (or mother wavelet),three topics are studied in this paper.Firstly,the numerical computation stability of dyadic wavelets is discussed with a new concept——the stableness,which enables us to measure the stabilizing ability in numerical inverse of wavelet;And then the stableness of a novel class of complex analytic wavelet——Y wavelet (whose quality factor is changeable)is analyzed.Finally,we investigate the orthogonal condition of Y wavelet.Theoretical analysis and results of numerical simulation show that:The stableness and frequency selectivity of wavelets contradict each other in wavelet analysis,but this problem can be mitigated to some extent by changing the scaling dilation parameter;The stability region of dyadic Y wavelet class is very narrow and limited by larger quality factor;It is impossible to construct an integral translation orthogonal basis by using Y wavelets,except that the real Y wavelet might exist on some integral translation orthogonal basis.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2000年第10期56-59,共4页
Acta Electronica Sinica
关键词
稳定性
信号分析
子波
品质因数
正交条件
Y-wavelet
stableness
dyadic scale
quality factor
orthogonal condition
