1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

342 CHAPTER 9 • Z·TRANSFORMS AND APPLICATIONS

Solution

Remark 9.4

When using the residue theorem to compute inverse z·transforms, the complex

form is preferred; i.e.,

z (2z -eia -e-ia)

3[xn] = 2 ( z - e•a. ) ( z - e-•a · )'

9.1. 3 T able of z-transform s

We list the following table of z..transforms. This table can also be used to find
the inverse z..transform.

Sequence z..transform

1 .5[n] 1

2 u[n) z-1 z

3 bn •z -b

4 b»-^1 u [n - l j z-b^1

5 e<>n z-ez 0

6 n (z-1)z 2

7 n2 $W l

8 nbn (•-bl' bz

9 ne'm •••

<·-·· >"

10 sin( an)

i(-l+e"•}z

2(e'•-z)(-l+e<• •)

11 bn sin( an)

ib -l+e'lio z

2 be••->)(-b+e •z)

12 cos( an)

13 bn cos( an)

Table 9.1 z-transforms of some common sequences.