4.14. Verify the accumulation property ( 4.25 ), that is,

R’ => R n {lzl > 1}

From Eq. ( 2.40 ) we have

n

y( n ] = E x [ k ] =x [ n ] * u( n J

k = -CX)

Thus, using Eq. ( 4.16 ) and the convolution property ( 4.26 ), we obtain

Y( z ) = X( z ) ( 1

1 2

_ 1 ) = X( z ) ( )

-z z- 1

with the ROC that includes the intersection of the ROC of X( z ) and the ROC of the z-transform of u[ n ]. Thus,

n 1 Z

1

E x [ k ] +-4 _ X( z ) = X( z )

k = -1 – z z – 1

R’ R n { l z l > I}