319 13.1 Definition and Examples Figure 13.5: Region of convergencc for the fiiriction X(z) from Kxnmplp 13.Y region of tmivrrgencc is cirrular licrc too, and its iadius is equal to tlie mngiiitiide of the pole In ccrmptirison to Examplc 13.2, wc irotice that the z-transform of thr riglit sided cxponential sequence (13A) arid the left-sided cxponmtiaI sequence (13.7) h v e the sarnt’ form and only thc regions of convergerice axe diffeierrt (Figiws 13.3 the region of corivergencc and 13.5) This eiriph M’ithout it a unique IVc are familiar wiih this sit uation from the l ~ p l a c ctransform In Exainp l ~ s4.1 arid 4.2 we corisiclcred lcft-sided mid right-sidtvi continuous-time signals tlint arc’ likewise orily ( ~ s t i ~ ~ ~ iby ~ ithe s ~ region i t ~ t ~of corivergence (see Fignres 4.3 arid 4.4) ne Wi cari iriterprct the individual points of the :-plane in a similar way t o the splane in Chapter 3.1.3 ti’ignrc 13.6 shon s the corresponding exponential secpen(*+’ zk for different values of z Tht valucs z = eJb’ on t,lie w i t circle correspond to thc cqtonential serim eJc’kwitlicorrstant amplitude: z = lei& to a series with constant values because eJok = l k =; 1, whilc z = - is the highest repiesentable frequency, 1wc.ai.w F ) x k = (- J ) k All other valiieq cm thc unit circle repr rit complex expotieni in1 oscillations ctf frcqiicncy with ?r < i l ic T c‘omplcx coiijngate values oi a r t distingms2ied by the tlirectioii of rotation Values of z = I’c~‘‘witlirri ihc unit circle (/ < 1) b ~ l o n gto a decaying exltoncntial stqucnce arid vdiies out.;idc the unit circlc ( T 1) belong t o c? growiiig exponelitis1 seqiieiice In Figure 13.6 the exponential srries z h are each oiily slrom7n for k This shooltf not lead t o the misintcrprelatiori that we are onlv dcalirig wit11 rnii1;uteral scquences since d s o for k < 0,z k f