多频率多函数正交小波基

Multi-frequency orthogonal wavelets generated by a finite set of functions

通过方向多分辨分析构造的由一个函数生成的多频率正交小波推广到由有限个函数生成的多频率小波 .给出由 n个函数的平移生成 V0 空间的正交基和由多个函数的平移生成 W0 空间的正交基的充分必要条件 。

Multi frequency wavelets, via directional multi resolution analysis and generated by a single function are extended to orthogonal wavelets generated by a finite set of functions. Necessary and sufficient conditions for translation of φ 1 ,..., φ n to form an orthogonal basis for V 0 and translation of a finite set of functions to form a orthogonal basis for W 0 (the orthogonal complement of V 0 in V 1 ) are derived. The construction of wavelets generated by a finite set of functions is given.