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8/14/2019 Chapter Three: The Impulse Response
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CHAPTERTHREE:
THEIMPUL
SERESPONSE
3.1
Introduction
There
latedconc
eptsofim
pulseresp
onse
andconvolution.
System
swithm
emory
haveimpulse
(or
unit-pul
se)responseswhicharenonzerofor
somefin
ite(butnonzero)rang
eoft(orn)
.
1
8/14/2019 Chapter Three: The Impulse Response
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CHAPTERTHREE:
THEIMPUL
SERESPONSE
3.2
Co
nvolutionFormofAnLSISystem
Unit-Puls
eResponseo
fAnLSISystem
Consider
alinear,shift-invariant,
causal(LSIC
)DT
system
escr
e
t
etransorm
atonoperator
.
(Figure3
.6(a)).
Letitsinputx[k]
betheunit-
pulse
functionx[k
]=[k]=
Assumingzeroinitialcondition,itsoutputis
then
givenby
2
1
k=0
0
k0
8/14/2019 Chapter Three: The Impulse Response
3/38
CHAPTERTHREE:
THEIMPUL
SERESPONSE
3.2
Con
volutionForm
ofAnLSISys
tem
Unit-PulseResponseof
AnLSISystem
y[k]=F[x[
k]]=F[[k]]h[k]
whereh[k]isdefinedas
theunit-pulseresponse(also
known
asteimp
useresponse.
Foracausasystemoneprop
ertyo
h[k]isim
mediatelyapparent.Since[
k]=0forallk