再谈对“杜氏积分”与“杜氏变换”的意见

Further Opinions on "Du Integral" and "Du Transform"

本文指明“杜氏积分”与“杜氏变换”在理论上将输入函数表述为时时截止的根本错误以及由此产生的后果.针对杜庆萱的“答”文提出的观点和存在的问题,经分析本文指出卷积积分和Duhamel积分可以应用于一切线性定常连续系统,不论其为线性瞬时系统还是线性记忆系统或是两者的混合系统;杜庆萱的“答”文中所求出的ρ_T(t)不是真正的单位门函数响应,其计算和結果都是错误的,h(t—T)、h_u(t—T)和ρ_T(t)都是或含有(t—T)的函数,因而“杜氏积分”与两种基本时域积分都是卷积积分;“杜氏变换”缺乏理论根据不能成立;数学推导证明,由卷积积分或Duhamel积分不能得“杜氏积分”,两者差一截止项h_u(O)x(t).

The radical mistake of 'Du Integral' and 'Du Transform', being to express the input functions as cutting off at any moment, and the results caused by this mistake are pointed out in this paper.To counter the ideals and problems posed by the paper [2], it is demonstrated that Convolution Integral can be used to all Linear Invarient Continuous Systems, including both the Linear Instantaneous Systems and the Linear Memory Systems or the Hybrid Systems of these two kinds of systems.ρ_T(t) obtained in paper [2] is not the correct Unit Gate Response, both of its calculation and result are incorrect.h(t-T), h_u(t-T) and ρ_T(t) are(or contain) the functions of(t-T), therefore 'Du Integral' as well as two kinds of the fundamental time-domain integral are convolution integrals.'Du Transform' is untenable due to lack of theoretical basis.It is proved by using mathematical derivation that Duhamel Integral can be obtained by Convolution Integral, these two integrals are equivalent to each other, but the Convolution Integral cannot lead to 'Du Integral', the difference of these two integrals is a cutting-off term h_u(0)x(t).