信号与系统中单位冲激函数教学方法研究

Study on teaching method of the unit impulse function

单位冲激函数的定义及其相关性质是信号与系统课程教学中的难点。文章兼顾工科学生的认知能力和冲激函数δ(t)数学定义的严谨性,由浅入深,从对冲激函数的物理性质的感性认知出发,而后从矩形脉冲函数序列极限引入冲激函数的抽样性,最后归于其广义函数的严格数学定义。该讲授方法有利于启发学生从形象思维到抽象思维,便于工科学生接受并理解。

The definition and property of the unit impulse function is a difficult teaching point in Signal and System. To go from the easy to the difficult, the rigorous mathematical definition of the function is reconciled with engineering students’ cognitive ability in this paper. The physical property of the function is introduced at first, then the sampling property of the function is derived through the limit of the sequence of rectangular impulse function. At last, the strict definition of the unit impulse function based on the distribution function is studied. This teaching method is easily understood and accepted by engineering students. Moreover, it prompts students to think from image thought to abstract thought.