Signal Processing and Linear Systems-B.P.Lathi copy

8 2 b y d iscretizing t he s ignal t hrough s ampling

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online