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《ACTA ELECTRONICA SINICA》 2000-10
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On the Stability and Orthogonal Conditions of a Novel Class of Wavelet

YUAN Xiao 1,2 ,HE Xiao hai 1,TAO De yuan 1 (1 College of Electronic Information,Sichuan Univ.,Chengdu 610064,China; 2 Dept.of Aeronautical Electronic Eng,The Air Force Univ.of Eng.,Xi′an 710038,China)  
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.
【CateGory Index】: TN941
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【References】
Chinese Journal Full-text Database 2 Hits
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【Co-citations】
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