8.Corrvoliition and Impirlse Hebponsc 162 Figure 8.9: Scaled delta inipnlbe ~ ~ l t i p l ~ c a twith i o n a ~ Q i i t i r i u oFimetion ~~s Froui the selcrtiw property, (8.21) This s i ateiiient is only true -just like selective property (8.13) for tuwtions f ( t ) that are contiiiuoiu a t t = In particnlar, the piot1itc.t of two dclta impulses ( i ) s j t ) is not peiinitted The investigation of tlic clelta impulse with the selective prop car1 bt espandctl to other properties, for exicniplc, forming a dcrivativc Diffwcntiat ion of S ( i ) by forrrririg tlir diffcrential quo~ieiilis of C O I I I S ~ not pc)ssilr)lc, a s tiw tlclta impulse c.lzrinot he differcwtiated Despite this, a comparable operatioii can iri fact, be used on distiibrrtions To tjlist ingiiish this from differeritiating ordinary functions, howevcr, the term derzliutton is used Tlir dcriwtivr of the delta irnpulse has the same iiotatiori as the synilml fot a derivative with IPspPct to tiinc wri 11 h ( t ) ‘&I explain what bhauld bc iinde1stood by this, we will again use the sclcctivr prijperty Under the iiittgral, thc drrivativc of d(t) ran bc transformcd using partial integration of thc corresponding continuous fiinc.fion, aitd (11 ivc p r o p i t y of the mdefinctl fiiricrion 8(t)c m be re.pretwiited by the effcc t, of a delta impnlse ( L ) -x r