Wiley signals and systems e book TLFe BO 320

12.3. Discrete-Timc Foiirirr Transform
m t l from t h i s

TVP

305

can dircctly obtain

Figure 12.6 shoivs 011 the lelt the first few vdues of this fqxmcritiwl series for it real
(1. and the right shows thc magnitude of the spectrum. T h e spedrurri is clearly
periodit with period 2n. As (12.36) does iiot convc'rgt' for (1 = I , the sprc'trim of
the [uri
fimrtioii (12.33) is iiot contaiiied in (12.36) ab a spc

1

ansform Qf a Rectangle Series
~ + w:mt
~ o to find the .F* t,rwnsform

x ( P of
) a rrctanglc scries wit11 length N
( 123 7 )

as showir in Figure 12.7. Inserting this inlo tlir tic4ining cquatiorl (12 13) Icads to

N-1
Figixrct 12 7: Rectangle serirs of length N

a. liriitc geometr ic wriw

(12.38)