浅析冲激信号与在奇异点处不连续信号的乘积  

A Pilot Discussion on the Product of Impulse and the Signal which Is Discontinuous at the Singularity Point

作　　者：姜小磊[1] 

机构地区：[1]华北电力大学计算机科学与技术学院,河北保定071003

出　　处：《电气电子教学学报》2008年第2期57-58,62,共3页Journal of Electrical and Electronic Education

摘　　要：众所周知,当x(t)在t0处连续时x(t)δ(t-t0)=x(t0)δ(t-t0),本文考察当x(t)在t0处不连续时处理x(t)δ(t-t0)的一种方式,即利用频域卷积定理求其频谱,结果是x(t)δ(t-t0)=1/2[x(t0-)+x(t0+)]δ(t-t0)。因为该式涉及广义函数的乘积,为了避免不一致和误解,本文只把它看作是其频域形式的时域简记,并且该式在应用时只在中间过程出现,最后结果中不会保留。本文把这个关系及其对偶形式用来方便地获得两个问题的解答:一是对连续时间信号采样时,信号在采样点处不连续如何处理;二是对信号通过理想频选滤波器,信号频谱在滤波器通带边缘存在冲激时如何确定输出。It is well known that if x（t） is continuous at to, then x（t）δ（t-t0） = in which x（t） is discontinuous at to is explored. By convolution theorem in x（t0）δ（t-t0）. Here the case the frequency domain, it is shown that x（t）δ（t-t0） = 1/2[x（t0）＋x（t0＋）]δ（t-t0）. To avoid possible confusion and inconsistence, this equation is understood only as the shorthand in the time domain for its ：corresponding frequency - domain equation , and in. the development of other formulas , only in the intermediate steps does it appear. This equation and its frequency-domain dual are useful to easily obtain solutions to two problems. First, in the sampling of a continuous - time signal , what value does the obtained discrete - time signal take on at the discontinuous point of the signal being sampled. Second, what is the output of an ideal frequency-selective filter to a signal whose spectrum contains impulse just at the edge of the passband of the filter.

关 键 词：冲激 采样 傅里叶变换 

分 类 号：TN911.6[电子电信—通信与信息系统]