Con~olut~ion arid Impiilsc Respoase One of the two step responses miist also be differentiatetl hcfort conivolut ion takes placc.. Alterriatively, the convolution of the step response ca
Trang 1182 8 Con~olut~ion arid Impiilsc Respoase
One of the two step responses miist also be differentiatetl hcfort conivolut ion takes placc Alterriatively, the convolution of the step response can be carried ont and their the rrsult can be dilTerentiater1 Equation (8.67) can easily be expanded
to cover N cascaded systems Tire coniplete step respoiisr is ohtaincd by t-fiffcr- enlisting the component step I or the complete prodixt of tonvohitioii
( N - 1) h i e s
O ~ V O ~ ~ t ion by
In Section 8.4.3 WY biicfly dealt with the ctdcul&ion of tlw couvohition integral This iwthod always works, biit it is cuinbersorne for funclions t h a t are rlrfiiied by mull iple cases, a5 tEic convolution integial takes a tliffereiit form tor each case, and
w e b must bc calculated indivithially
In this section we will desvxibe a 5implc mctliod that is well suited to signals with corisl ant scvtions, rzs it is not necessary to cwduate tlir conivolution integral for tlrcse sections With sortie practicP it i s possible to find the convolution product with this method, called convolut/on hy insperf7on ‘ r h ~ reader should try to acquire this skill, because it bririgs an intuitive Luldeistandirig of the c oiivolutiori operation wliich is esseiitial fo1 practical work
To tiemonstratc the process we will tonsidn tlre two rectanglP c;ignaIs from
Figure 8.27 and fiist evaluate thc convolittion integral as in Section 8.4.3
1
*-
t
\
Figure 8.27: Examplc 8.6 of‘ coiivdution by inspe~ctioii The two signals from Figure 8.27 are defined by the func‘tioris
2 o < t < a
arid y(t) = 0 otherwise
1 o 5 t < a
‘To calculate i,he conk olut ion integral, however both sigiids rmst bc fulictkms of