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． The two-scale difference equation is extended to a general two-scale integral equation, and the existence conditions of the solution and its solution are studied. On this basis, the concept of semi-continuous wavelet transform is proposed, its fast tower decomposition algorithm and frame-based synthesis algorithm are given, and three semicontinuous wavelet function classes are constructed and applied in the processing of broadband correlation. Semi-continuous wavelet transform based on two-scale integral equation preserves the advantages of continuous wavelet transform and discrete wavelet transform, and overcomes the shortcomings.