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 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 - ~ 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 tralisfoinl arid the Fouricr trilnsform vcv rccognisc that (13.10) (13.1I )