奥本海默《信号与系统课件》

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1、GeneratedbyFoxitPDFCreator©FoxitSoftwarehttp://www.foxitsoftware.comForevaluationonly.2.3PropertiesofLinearTime-InvariantSystemsWangZhengyongCollegeofElectronicsandInformation,SichuanUniversityGeneratedbyFoxitPDFCreator©FoxitSoftwarehttp://www.foxitsoftware.comForevaluationonly

2、.一.卷积积分与卷积和的性质1.交换律(Thecommutativeproperty)：yn()xn()hn()xkhnk()()kxnkhk()()hn()xn()kyt()xt()ht()x()(ht)dxt()()hdht()xt()GeneratedbyFoxitPDFCreator©FoxitSoftwarehttp://www.foxitsoftware.comForevaluationonly.hn()xn()xt()yt()ht()yt()ht()xt(

3、)xn()yn()hn()yn()结论：一个单位冲激响应是ht()的LTI系统对输入信号xt()所产生的响应，与一个单位冲激响应是xt()的LTI系统对输入信号ht()所产生的响应相同。GeneratedbyFoxitPDFCreator©FoxitSoftwarehttp://www.foxitsoftware.comForevaluationonly.2.分配律(Thedistributiveproperty)：xn()[()hnhn()]xn()hn()xn()hn()1212xt()[()htht()]xt()ht()x

4、t()ht()1212xn()yn()xn()[()hnhn()]12hn()hn()xt()12yt()xt()[()htht()]12ht()ht()12ht()1xn()hn()1hn()1xn()yn()xt()yt()hn()2xnhn()()ht()22GeneratedbyFoxitPDFCreator©FoxitSoftwarehttp://www.foxitsoftware.comForevaluationonly.结论：两个LTI系统并联，其总的单位脉冲(冲激)响应等于各子系统单位脉冲(冲激)响应之和。3

5、.结合律(Theassociativeproperty):[()xnhn()]hn()xn()[()hnhn()]1212[()xtht()]ht()xt()[()htht()]1212GeneratedbyFoxitPDFCreator©FoxitSoftwarehttp://www.foxitsoftware.comForevaluationonly.xt()xt()ht()yt()[()xtht()]ht()112ht()ht()12xn()yn()[()xnhn()]hn()hn()hn()1212xt()

6、yt()xt()[()htht()]12ht()ht()12xn()yn()xn()[()hn1hn2()]hn()hn()12结论：•两个LTI系统级联时，系统总的单位冲激(脉冲)响应等于各子系统单位冲激(脉冲)响应的卷积。•由于卷积运算满足交换律，因此，系统级联的先后次序可以调换。GeneratedbyFoxitPDFCreator©FoxitSoftwarehttp://www.foxitsoftware.comForevaluationonly.xn()hn()hn()xn()hn()hn()1221xt()ht(

7、)ht()xt()ht()ht()1221xn()yn()hn()hn()xt()12yt()ht()ht()12xn()yn()hn()hn()xt()21yt()ht()ht()21产生以上结论的前提条件：①系统必须是LTI系统；②所有涉及到的卷积运算必须收敛。GeneratedbyFoxitPDFCreator©FoxitSoftwarehttp://www.foxitsoftware.comForevaluationonly.2如：xt()平方yt()2()xt乘2若交换级联次序，即成为：2xt()yt()4()xt乘2平方显然

8、与原来是不等价的。因为系统不是LTI系统。GeneratedbyFoxitPDFCreator©FoxitS