8 ~ i ~ t ~ ~ ~ a ~ ~ r s First of all we would likci to know alxtut tlrr plopertips of a system tliit l l ~ sthe step fimriiori E ( t ) as its irnpulsr ~ C ~ ~ P O I I Sfioiii C the convolution of cjt) ancl z(t), wc find that with (8.39) tlic oiitpnt signal is yjf) = E ( f ) * r(f)= E(l - z)z( 7-1 tlr (8.50) -x (8.5i) wci c m leavc oul 1he p fuwtion iinder the intcy-gal in (8.X)) avid in over the values of T for ~ b h r c hi ( f - E ) = I , that is, between - It -y ( t ) = E ( t ) r ( t )= 1 ( z) d z (8.52) h A systein with the response ~ ( f A)S inipulsc~responsc tlicretole leads to an integxcition ol the inyA, signal, or in slrort: it i s ail ii1tegr:ctor This rewlt w;ts also found iii Section S.3.4.3, wlierc V.P said thilt iirtegrating it clelt n iiupulse yirldrd a si,ep fitiic.lion Figui 8.19 shows a b1oc.k diagram of irn integrator arid also i t s resporihe to a delLa im~mlseat the input The coriwlutioir 11) eh Figure 19: An integiator rt?sporrtls to a delta irripulse w i t h a s t c y Cuiictiori