Wiley signals and systems e book TLFe BO 337

i0
Close rdationships exist Ixhtwetw t lie :-transform
lmow.

c t d

other trrinsftorrns WP already

The z-transform and tlir Fouriei t iansforni .Fx of a sc,ritxs are closel~~
, like the Lapinct. transform ancl Iht- Fo-Lrricr 1 rairsforrn F of R
Is-time signal (bee Chapter 9.3).
[k]has been cieatrcl 1)y saiiipliirg a continuoiis-tiiiic signal x(t),
tlir valnrs of I [ A J c m be iriterprctcd as thc wciglit ings of individual irripii
in
iinpulsc. train (see Figurt, 12.9). Bet
t h e Laplace trwrisforin X ( s
G{ r ( t ) } ant1 thc 25jfoririX ( z ) = Z{
there iritist likewise lie a close
corinect ioxi.

We will IX)W exitniii~pmore precisely thcse relstiormshipr bet ween the iridividttal
t rnnsforms.

When the -.-trarrsfotorm of a sequence z[k1 i s only calculated for \dues
ciiclc
,It E R ,
i -

~

2

on the unit
(13.9)

tlw Fourickr. transform of ttii
qucnce is irnmt~diatelyo bhined. By cornpar iiig t lie
instructions f o r cdmi ng the 3 tralisfoinl arid the Fouricr trilnsform vcv rccognisc
that

(13.10)

(13.1I )