Wiley signals and systems e book TLFe BO 326

3J 1

12.5. Propcrties of the .F%
Transform

Exarnpla 12.4

We have iilreatiy rrrct the trarrsforni pair (12.24):

I;korn (12.56), wc' expect conjugate synimetrical spectra for discrtitc-time signals
with real values. In p a r t i d a r ,

(12.58)

cim only fuliill tliese c-oriclitions, for example. if R = T , for
i ~ n ( X ( e J ' ~))O

I

(12 .59)

Li

7 he spcctrum of a series with real valiirs is therefore real for
i2 = . . . - 3 ~- - ,~ , 7 r , 3 7 .~., .. The Lransform pairs (12.20), (12.33) niid (12.39)
confirm this.