终值定理 若:因果信号x()+X(z), 则imx(n)=lim[(二-1)X(=) 证明::z{x(n+1)-x(m)}=zX(z)-x(0)-X(z) (二-1)X(=)-zX(0) limn[(z-1)X()=lm{Z[x(n+1)-x(m)]+x(0) im∑[x(m+1)-x(m) n=0 =[x(1)-x(0)]+[x(2)-x(1)+…+[x(m)-x(n-1)+…+x(0) limn[(z-1)X(z)=x(∞)
X 第 1 终值定理 页 若: 因果信号x(n) → X(z), 1 lim ( ) lim[( 1) ( )] n z x n z X z → → = − Z x n x n zX z zx X z { ( 1) ( )} ( ) (0) ( ) + − = − − 1 1 lim[( 1) ( )] lim{ [ ( 1) ( ) } ] (0) z Z z X z Z x n x n zx → → − = + − + = − − ( 1) ( ) (0) z X z zx 则： 证明: 1 lim[( 1) ( )] ( ) z z X z x → − = 1 0 lim [ ( 1) ( )] (0) n z n x n x n z x − → = = + − + = − + − + + − − + + [ (1) (0)] [ (2) (1)] [ ( ) ( 1)] x x x x x n x n x(0) n→∞