Zero and pole The z-transform is most useful when the infinite sum can be expressed in closed form, usually a ratio of polynomials in z(or z). x立z P(2) =-o0 Zero:The value of z for which X()=0 Pole:The value of z for which X()=oo 1313 Zero and pole ( )   ( ) n ( ) n P z X z x n Q z z  =− − = =  ◆Zero: The value of z for which X(z) = 0 ◆The z-transform is most useful when the infinite sum can be expressed in closed form, usually a ratio of polynomials in z (or z-1 ). ◆Pole: The value of z for which X(z) = 