Wiley signals and systems e book TLFe BO 312

aling v-ith some simple disrrtlte siguals; x w Itnow thrir continuous-tinit coiirti carparts 'L'heso sigrials are the inipnlsc, expoiieiitial series ~ The discrete unit imp-tllse is defined by (L2.3) Figure 12.2 shows thib series The discrele unit impulse Iiah the helertiw propel t y "U I (12.4) that, r i z ~1 ) easily ~ checked k Figure 12.2:Discrc4t u r r i t impulse Comparing (,hiswith the relwtivc property of f , h continuoiih-time ~ delta impulse shows a close relatioiiship between the two: (12.5) Integration with resp to tlie continuous variable z in (12.5) correspoiids o smiiniatioii with respect to tJie di ete inrlcpcirdeiit variwhle K ; in (12.4) TVe will sec that replacing integration in the clefinit,ion of a continuous sigrlal with summat ion often leads to the equivalent discrete signal Thcre is a m o l e \ significant, diffcrence bet8weerit,lw disrrete nnit impulse arid ~ I I P contiinioiis deka impulse: the unit, irnpulse 6jk] is not a distribution For k = it has the finite valiie 6[0]= I which makes calculations simple In contrast to thcl continuous tlelta irripiilse ( t ) , ilie unit impulse a forriitila and does not wquirc the use of the SP