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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

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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

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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