Wiley signals and systems e book TLFe BO 333

I D . The a-‘l’ransform

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I5giirc. 13.3: Region of convorgmrt. of t t i t ~fundiorl X ( z ) from Example 13.2

For U = I the seyiicnct’ x[kj represents the unit step finictiori &[kj from ( 1 2.6).
Its z-transform i s
2
Z{E[kj}= (13.61
z - I ’ 1x1 > 1

The z-transform of t,hc a lehitled exponriil id s e q i m i c e from Figure 13.4
.r[k-= -ak c[ k - 11, n F Q

(13.7)

is

Figure 13.4: Exariiple of a. left-hidetl expoiicntinl scqiwricc

This siim convcrgcs for /z/i[ U / , which riiwiis all valiiw of z in the cornplcx
planc that licl witliiri a circle of radius a (see Figure 13.5). Tlie houndary of thc