信号系统中冲击函数另一种图形化表示的研究

Research on Another Graphical Representation of Impulse Functions in Signal Systems

摘要: 冲击函数又叫冲击信号，是信号系统和通信原理中常用的理想采样信号，最初是用来描述某些物理现象需要用一个超级短的时间，单取值极大现象的一种函数。单位冲击函数的图像就是一个冲击脉冲，但是如果单位冲击函数乘以一个常数以后，这样的冲击函数的图形仍然是一个冲击脉冲，而两个冲击脉冲无法在图形上区分冲击的大小，两者在图像的表示上一模一样。本文通过对冲激函数进行变量代换，然后再进行极坐标变换，最后在极坐标下，对冲击函数进行图形化表示，从而实现在图形上区别不同大小的冲击函数。进而提出将除以0看成一种广义变换，该变换的结果就是冲击函数这一猜想，并验证这一猜想。

Abstract: The impact function, also called the impact signal, is an ideal sampling signal commonly used in signal systems and communication principles. It was originally used to describe certain physical phenomena that require a super short time and a single maximum value. The graph of the unit shock function is a shock pulse, but if the unit shock function is multiplied by a constant, the graph of such a shock function is still a shock pulse, and the two shock pulses cannot graphically distinguish the size of the shock. The representation of the images is exactly the same. This paper realizes graphically distinguishing impact functions of different sizes by substituting variables for the impulse function, then performing polar coordinate transformation, and finally graphically representing the impulse function in polar coordinates. Then the conjecture that dividing by 0 is regarded as a generalized transformation, and the result of the transformation is the impact function is proposed, and this conjecture is verified.