连续信号和离散信号的卷积求和的闭式求解

Evaluate the Convolution Integral and Convolution Sum Use Compact Formula

连续信号的卷积积分和离散信号的卷积求和是线性时不变系统分析的基本时域计算方法。目前国内和国外出版的《信号与系统》教材,特别是电子工业出版社出版的两位著名学者Haykin Simon.和Alan V.Oppenheim分别写的教材《Signals and Systems》都采用图解的方法求解连续信号的卷积积分和离散信号的卷积求和。在本文中提出的闭式求解法避免用图解确定积分限和积分存在区间等问题,使连续信号的卷积积分和离散信号的卷积求和可以直接根据定义算出结果。

Convolution integral and convolution sum are principal methods in the linear time invariant systems analysis. At present, many text books that have been published in the my home country or foreign country, especially the Signals and Systems writing by Oppenheim A V and Signals and Systems writing by Haykin Simon, introduced the methods by use of the graph to determine the up limit, low limit and the exist interval of the integral or convolution sum. The closed methods that evaluate the convolution integral and convolution sum avoid to determine the up, low limits and the duration of the convolution integral and convolution sum by means of the graph, So that, the convolution integral and convolution sum according to the definition can be evaluated directly.