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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 from the construction conditions of the fundamental function (mother wave) of wavelet analysis, this paper proposes the purpose of this paper.In this paper, the general problems of numerical stability of wavelet analysis are discussed, and the concept of stability is introduced to describe the stability of the inversion of mother wave data. The stability of a complex analytical mother wave --- Y - mother wave whose quality factor can be controlled is studied. Finally, the orthogonal conditions of the Y - mother wave are analyzed.Theoretical analysis and numerical results show that the stability of the mother wave and its frequency selection However, the contradictory between the Y - mother wave and the Y - mother wave is very narrow due to the limitation of the quality factor. However, , There is no orthogonal integer shift basis, only the real part of the Y - mother wave (ie real Y - mother wave) has an orthogonal integer shift basis.