系统是 LTI 系统吗?y[n]=x[n]+2=T{x[n]}y[n]=x[n]+2=T{x[n]}
线性: α⋅T{x1[n]}+β⋅T{x2[n]}=T{α⋅x1[n] +β⋅x2[n]}α⋅(x1[n]+2)+β⋅(x2[n]+2)=α⋅(x1[n]+2)+β⋅(x2[n]+2)α⋅T{x1[n]}+β⋅T{x2[n]}=T{α⋅x1[n] +β⋅x2[n]}α⋅(x1[n]+2)+β⋅(x2[n]+2)=α⋅(x1[n]+2)+β⋅(x2[n]+2)
时不变性: y1[n]=y[n−n0]=x[n−n0]+2x2[n]=x1[n−n0]y2[n]=T{x2[n]}=x[n−n0]+2y1[n]=y2[n]y1[n]=y[n−n0]=x[n−n0]+2x2[n]=x1[n−n0]y2[n]=T{x2[n]}=x[n−n0]+2y1[n]=y2[n]
所以我会说它是一个 LTI 系统,对吗?
添加常数的系统很少是线性的。如果您有两个输入和,每个输入都会得到常数,因此它们的组合会得到常数两次。而输入仅获得一次常量。x1x1x2x2x1+x2x1+x2