双尺度积分方程与半连续子波变换

Two scale intergral equation and semi continuous wavelet transform

把双尺度差分方程推广为一般的双尺度积分方程，研究了其解的存在性条件及解的求法．在此基础上，提出了半连续子波变换的概念，给出了其快速塔式分解算法和基于框架的综合算法，构造了３个半连续子波函数类，并应用于宽带相关处理中．基于双尺度积分方程的半连续子波变换保留了连续子波变换和离散子波变换的优点，克服了其缺点．

In this paper, we extend the two scale difference equation to the two scale integral equation and study its solution existence condition and the method to solve it. On the basis of the two scale integral equation, the semi continuous wavelet transform, a new type of wavelet transform, is proposed, meanwhile its pyramidal decomposition algorithms and synthetic algorithms based on the frame are given. Finally, three kinds of semi continuous wavelet functions are constructed and some applications are given in wideband correleation processing.