一种构造正交小波基的新方法

给出了不须验证多尺度分析条件的正交尺度函数新的构造定理，并进行了证明。由此导出了正交小波基构造方法，并给出了一个构造实行。

A Different Way for Constructing Orthonormal Wavelet Bases

Daubechies did much on application of wavelet theory to engineering problems L7J'Though Mallat gave a generally accepted method, based on multiresolution analysis, on constructing orthonormal wavelet bases L4), there are certain conditions under which a differentmethod presented in this paper can be more effective.Our method mares use of the well known Lebesgue theorem and Fatou's Lemma in theory of function of real variable to construct orthonormal wavelet bases. Our construction requires a theorem that is re18ted to inequality (3) and eqs. (4) through (6). One example,which gives actually the orthonormal wavelet bases needed in our research on vibration signalanalysis, shows that our construction method is simple and convenient.