小波系数与尺度的关系

Relations of Coefficients of Wavelet Transform and Scale

在总结了函数空间L2(R)与小波变换系数空间l2的关系的基础上,分析了Cn,α(R)空间的函数的小波变换系数的模极大值随尺度变化的关系,给出了一个比引理的条件较弱的条件,并得到了相应的结论.另外,在小波基函数满足一定正规性,被变换的函数有无穷阶导数的情况时,分析了小波变换系数的模极大值与尺度的变化关系.这为用小波变换分析函数或信号的特性提供了理论基础.

Based on analyzing the relation between the space L2（R） and wavelet transform coefficients space l^2 , a condition than lemma is presented with the same conclusions as lemma, with respect to the relation of the wavelet transform coefficients of a function belonging to the space Cn,α（R） varying with the scale. Additionally, the relation of the wavelet transform coefficients varying with the scale is obtained on the condition that the wavelet bases functions subject to certain regularity and transformed functions are differential arbitrarily. These provide theory bases for analyzing properties of function or signal by wavelet analysis.