卷积积分的快速分段和定限方法

A Fast Segmentation and Definite Bounds Method of Convolution Integral

卷积积分在积分变换、控制理论、信号与系统以及电路分析等学科中应用广泛,是一个重要的数学工具.虽然卷积积分的计算方法较多,但要准确计算出卷积积分并非易事,正确地分段和定限是计算卷积积分的两大难点.从卷积积分的定义出发,经严密的数学推导获得一种卷积积分的快速分段和定限方法.在此基础上,进一步绘制出卷积积分的快速分段和定限图,使得卷积积分的分段和定限更加直观易行.实例表明,应用快速分段和定限法能够快速准确地求解卷积积分.

Convolution integral is an important mathematical tool widely used in many subjects such as integral transform, control theory, signal and system, and the circuit analysis. Although there are many convolution integral calculation methods,it is still hard to accurately calculate convolution integral. Two difficulties lies in：how to correctly determine the time segmentations of the convolution results and the integral upper and lower bounds in each segmentation called for short segmentation and definite bounds. Starting from the definition of convolution integral,a convolution integral fast segmentation and definite bounds method is proposed by strict mathematical deduction. On this basis,a convolution integral of fast segmentation and definite bounds figure is drawn, which makes the segmentation and definite bounds more intuitive and easy.Some examples show that the fast segmentation and definite bounds method can rapidly and accurately solve the convolution integral.