Unformatted text preview: eviation
from t he ideal is caused by t he fact t hat we have used a nonzero sampling interval T . As
T a pproaches zero, the o utput yet) approaches t he desired o utput u(t). •
6 E xercise E 8.8
Design a discrete-time system, such as in Fig. 8.2, to integrate continuous-time signals.
= J (t). ApproxHint: I f J (t) and yet) are the input and the output of an integrator, then
imation (similar to that in Example 8.7) of this equation at t = k T yields y[kJ - y[k - lJ = TJ[kJ.
Show a realization of this system. 'V ¥. B y u sing d igital c omputers w hich r eadily p erform t he o perations o f a dding,
m ultiplying, a nd d elaying. M inicomputers a nd m icroprocessors a re well s uited
for t his p urpose, e specially for signals w ith f requencies below 100 k Hz. 2. B y u sing s pecial-purpose t ime-delay d evices t hat h ave b een d eveloped i n t he
l ast t wo d ecades. T hese i nclude m onolithic M OS c harge-transfer d evices ( CTD)
s uch a s c harge-coupled d evices ( CCD) a nd b ucket b rigade d evices ( BBD),
w hich a re i mplemented o n s ilicon s ubstrate a s i ntegrated c ircuit e lements. I n
a ddition, t here a re s urface a coustic wave (SAW) devices b uilt o n p iezoelectric
s ubstrates. S ystems u sing t hese d evices a re less expensive b ut a re n ot a s reliable o r a s a ccurate a s t he d igital s ystems. D igital s ystems a re p referable for
signals below 100 kHz. S ystems u sing C TD a re s uitable a nd c ompetitive w ith
t hose u sing S AW devices i n t he f requency r ange 1 kHz t o 20 M Hz. A t f requencies h igher t han 20 M Hz, SAW devices a re p referred a nd a re t he o nly r ealistic
choice for frequencies h igher t han 50 M Hz. S ystems u sing S AW d evices w ith
f requencies in t he r ange o f 10 M Hz t o 1 G Hz a re i mplemented r outinely.1 T here is a b asic d ifference b etween c ontinuous-time s ystems a nd a nalog s ystems. T he s ame is t rue o f d iscrete-time a nd d igital s ystems. T his is fully e xplained
i n Secs. 1.7-6 a nd 1 .7-7.t F or h istorical r easons, d igital c omputers ( rather t han t imedelay e lements, s uch a s C CD o r S AW devices) w ere u sed i n t he r ealization o f e arly
d iscrete-time s ystems. B ecause o f t his f act, t he t erms digital filters a nd discretetime systems a re u sed s ynonymously i n t he l iterature. T his d istinction is i rrelevant
i n t he a nalysis o f d iscrete-time s ystems. F or t his r eason, i n t his b ook, t he t erm digital filters i mplies discrete-time systems, a nd a nalog filters m eans continuous-time
systems. M oreover, t he t erms C /D ( continuous-to-discrete-time ) a nd D /C will b e
u sed i nterchangeably w ith t erms A ID ( analog-to-digital) a nd D IA, r espectively. A dvantages o f Digital Signal P rocessing
1. D igital f ilters have a g reater d egree o f p recision a nd s tability. T hey c an b e
p erfectly d uplicated w ithout h aving t o w orry a bout c omponent v alue t olerances
a s i n a nalog case.
2. D igital f ilters a re m ore flexible. T heir...
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