《電子與通信工程專業(yè)英語》課件第1章

Unit1TheCommunicationProcessNEWWORDSANDPHRASES

NOTES EXERCISES

參考譯文

EXTENSIVETEXT

Today,communicationentersourdailylivesinsomanydifferentwaysthatitisveryeasytooverlookthemultitudeofitsfacets.Thetelephonesatourhands,theradiosandtelevisionsinourlivingrooms,thecomputerterminalswithaccesstotheInternetinourofficesandhomes,andournewspapersareallcapableofprovidingrapidcommunicationsfromeverycorneroftheglobe.Communicationprovidesthesenseforshipsonthehighseas,aircraftinflight,androcketsandsatelliteinspace.

Communicationsthroughawirelesstelephonekeepsacardriverintouchwiththeofficeorhomemilesaway.Communicationkeepsaweatherforecasterinformedofconditionsmeasuredbyamultitudeofsensors.Indeed,thelistofapplicationsinvolvingtheuseofcommunicationinonewayoranotherisalmostendless.

Inthemostfundamentalsense,communicationinvolvesimplicitlythetransmissionofinformationfromonepointtoanotherthroughasuccessionofprocesses,asdescribedhere:

(1)

Thegenerationofamessagesignal:voice,music,picture,orcomputerdata.

(2)

Thedescriptionofthatmessagesignalwithacertainmeasureofprecision,byasetofsymbols:electrical,aural,orvisual.

(3)

Theencodingofthesesymbolsinaformthatissuitablefortransmissionoveraphysicalmediumofinterest.

(4)

Thetransmissionoftheencodedsymbolstothedesireddestination.

(5)

Thedecodingandreproductionoftheoriginalsymbols.

(6)

There-creationoftheoriginalmessagesignal,withadefinabledegradationinquality;thedegradationiscausedbyimperfectionsinthesystem.

Thereare,ofcourse,manyotherformsofcommunicationthatdonotdirectlyinvolvethehumanmindinrealtime.Forexample,incomputercommunicationsinvolvingcommunicationbetweentwoormorecomputers,humandecisionsmayenteronlyinsettinguptheprogramsorcommandsforthecomputer,orinmonitoringtheresults.

Irrespectiveoftheformofcommunicationprocessbeingconsidered,therearethreebasicelementstoeverycommunicationsystems,namely,transmitter,channel,andreceiver,asdepictedinFig1.1.Thetransmitterislocatedatonepointinspace,thereceiverislocatedatsomeotherpointseparatefromthetransmitter,andthechannelisthephysicalmediumthatconnectsthem.Thepurposeofthetransmitteristoconverterthemessagesignalproducedbythesourceofinformationintoaformsuitablefortransmissionoverthechannel.However,asthetransmittedsignalpropagatesalongthechannel,itisdistortedduetochannelimperfection.Moreover,noiseandinterferingsignals(originatingfromothersources)areaddedtothechanneloutput,withtheresultthatthereceivedsignalisacorruptedversionofthetransmittedsignal.Thereceiverhasthetaskofoperationonthereceivedsignalsoastoreconstructarecognizableformoftheoriginalmessagesignalforauser[1].Fig1.1Elementsofacommunicationsystem

Therearetwobasicmodesofcommunication:

(1)

Broadcasting,whichinvolvestheuseofasinglepowerfultransmitterandnumerousreceiversthatarerelativelyinexpensivetobuild.Hereinformation-bearingsignalsflowonlyinonedirection.

(2)

Point-to-pointcommunication,inwhichthecommunicationprocesstakesplaceoveralinkbetweenasingletransmitterandareceiver.Inthiscase,thereisusuallyabidirectionalflowofinformation-bearingsignals,whichrequirestheuseofatransmitterandreceiverateachendofthelink.

Thebroadcastingmodeofcommunicationisexemplifiedbyradioandtelevision,andtheubiquitoustelephoneprovidesthemeansforoneformofpoint-to-pointcommunication.

Allthesedifferentcommunicationsystemsaswellasothersnotmentionedhereshareacommonfeature:Theunderlyingcommunicationprocessineachandeveryoneofthemisstatisticalinnature.Indeed,itisforthisimportantreasonthatmuchofthisbookisdevotedtothestatisticalunderpinningsofcommunicationsystems.

1．PrimaryCommunicationResources

Inacommunicationsystem,twoprimaryresourcesareemployed:transmittedpowerandchannelbandwidth.Thetransmittedpoweristheaveragepowerofthetransmittedsignal.Thechannelbandwidthisdefinedasthebandoffrequenciesallocatedforthetransmissionofthemessagesignal.Ageneralsystemdesignobjectiveistousethesetworesourcesasefficientlyaspossible.Inmostcommunicationchannels,oneresourcemaybeconsideredmoreimportantthantheother.Wemaythereforeclassifycommunicationchannelsaspowerlimitedorbandlimited.Forexample,thetelephonecircuitisatypicalband-limitedchannel,whereasaspacecommunicationlinkorsatellitechannelistypicallypowerlimited.

Whenthespectrumofamessagesignalextendsdowntozeroorlowfrequencies,wedefinethebandwidthofthesignalasthatupperfrequencyabovewhichthespectralcontentofthesignalisnegligibleandthereforeunnecessaryfortransmittinginformation.Forexample,theaveragevoicespectrumextendswellbeyond10kHz,thoughmostoftheaveragepowerisconcentratedintherangeof100to600Hz,andabandfrom300to3100Hzgivesgoodarticulation.Accordingly,wefindthattelephonecircuitsthatrespondwelltothislatterrangeoffrequenciesgivequitesatisfactorycommercialtelephoneservice.

Anotherimportantpointthatwehavetokeepinmindistheunavoidablepresenceofnoiseinacommunicationsystem.Noisereferstounwantedwavesthattendtodisturbthetransmissionandprocessingofmessagesignalsinacommunicationsystem.Thesourceofnoisemaybeinternalorexternaltothesystem.

Aquantitativewaytoaccountfortheeffectofnoiseistointroducesignal-to-noiseratio(SNR)asasystemparameter.Forexample,wemaydefinetheSNRatthereceiverinputastheratiooftheaveragesignalpowertotheaveragenoisepower,bothbeingmeasuredatthesamepoint.ThecustomarypracticeistoexpresstheSNRindecibels(dBs),definedas10timesthelogarithm(tobase10)ofthepowerratio.Forexample,signal-to-noiseratiosof10,100and1,000correspondto10,20,and30dBs,respectively.

2．SourceofInformation

Thetelecommunicationsenvironmentisdominatedbyfourimportantsourcesofinformation:speech,music,pictures,andcomputerdata.Asourceofinformationmaybecharacterizedintermsofthesignalthatcarriestheinformation.Asignalisdefinedasasingle-valuedfunctionoftimethatplaystheroleoftheindependentvariable;ateveryinstantoftime,thefunctionhasauniquevalue.Thesignalcanbeone-dimensional,asinthecaseofspeech,music,orcomputerdata;two-dimensional,asinthecaseofpictures;three-dimensional,asinthecaseofvideodata;andfour-dimensional,asinthecaseofvolumedataovertime.Inthesequel,weelaborateondifferentsourcesofinformation.

(1)Speechistheprimarymethodofhumancommunication.Specifically,thespeechcommunicationprocessinvolvesthetransferofinformationfromaspeakertoalistener,whichtakesplaceinthreesuccessivestages:

①Production.Anintendedmessageinthespeaker’smindisrepresentedbyaspeechsignalthatconsistsofsounds(i.e.,pressurewaves)generatedinsidethevocaltractandwhosearrangementisgovernedbytherulesoflanguage.

②Propagation.Thesoundwavespropagatethroughtheairataspeedof300m/s,reachingthelistener’sears.

③Perception.Theincomingsoundsaredecipheredbythelistenerintoareceivedmessage,therebycompletingthechainofeventsthatculminateinthetransferofinformationfromthespeakertothelistener.

Thespeech-productionprocessmaybeviewedasaformoffiltering,inwhichasoundsourceexcitesavocaltractfilter.Thevocaltractconsistsofatubeofnonuniformcross-sectionalarea,beginningattheglottis(i.e.,theopeningbetweenthevocalcords)andendingatthelip.Asthesoundpropagatesalongthevocaltract,thespectrum(i.e.,frequencycontent)isshapedbythefrequencyselectivityofthevocaltract;thiseffectissomewhatsimilartotheresonancephenomenonobservedinorganpipes.Theimportantpointtonotehereisthatthepowerspectrum(i.e.,thedistributionoflong-termaveragepowerversusfrequency)ofspeechapproacheszeroforzerofrequencyandreachesapeakintheneighborhoodofafewhundredhertz.Toputmattersintoproperperspective,however,wehavetokeepinmindthatthehearingmechanismisverysensitivetofrequency.Moreover,thetypeofcommunicationsystembeingconsideredhasanimportantbearingonthebandoffrequenciesconsideredtobe“essential”forthecommunicationprocess.Forexample,asmentionedpreviously,abandwidthof300to3100Hzisconsideredadequateforcommercialtelephoniccommunication.

(2)

Thesecondsourceofinformation,music,originatesfrominstrumentssuchasthepiano,violin,andflute.Thenotemadebyamusicalinstrumentmaylastforashorttimeintervalasintheprocessingofakeyonapiano,oritmaybesustainedforalongtimeintervalasintheexampleofafluteplayerholdingaprolongednote.Typically,musichastwostructures:amelodicstructureconsistingofasetofsimultaneoussounds.Likeaspeechsignal,amusicalsignalisbipolar.However,amusicalsignaldiffersfromaspeechsignalinthatitsspectrumoccupiesamuchwiderbandoffrequenciesthatmayextenduptoabout15kHz.Accordingly,musicalsignalsdemandamuchwiderchannelbandwidththanspeechsignalsfortheirtransmission.

NEWWORDSANDPHRASES

aural adj. 聽覺的

degradation n. 降級(jí)，退化

imperfection adj. 不完整性，非理想性

ubiquitous adj. 無所不在的；普通的

underpinning n. 基礎(chǔ)，支柱，支撐

articulation n. 清晰度

decibel n. 分貝

logarithm n. [數(shù)]對(duì)數(shù)

vocaltract 聲道

decipher vt. 譯解(密碼等)，解釋

glottis n. 聲門

resonance n. 共鳴，諧振，共振

prolonged adj. 延長(zhǎng)的，拖延的

melodic adj. 有旋律的，調(diào)子美妙的

powerspectrum 功率譜

NOTES

[1]Thereceiverhasthetaskofoperationonthereceivedsignalsoastoreconstructarecognizableformoftheoriginalmessagesignalforauser.

“soasto”這里翻譯為“如此……以至……”。“recognizableform”譯為“可識(shí)別的形式”。

本句可譯為：接收器的任務(wù)是對(duì)接收到的信號(hào)進(jìn)行重建，使其成為用戶能辨識(shí)的原始信息信號(hào)的形式。

EXERCISES

I．Translatethefollowingwordsorphrases.

spectrumofamessagesignal goodarticulation thehighseas

signal-to-noiseratio(SNR) independentvariable vocaltract

點(diǎn)到點(diǎn)通信 光柵掃描 消隱脈沖

II．TranslatethefollowingparagraphsintoChinese.

(1)

Thetransmitterislocatedatonepointinspace,thereceiverislocatedatsomeotherpointseparatefromthetransmitter,andthechannelisthephysicalmediumthatconnectsthem.Thepurposeofthetransmitteristoconverterthemessagesignalproducedbythesourceofinformationintoaformsuitablefortransmissionoverthechannel.However,asthetransmittedsignalpropagatesalongthechannel,itisdistortedduetochannelimperfection.Moreover,noiseandinterferingsignals(originatingfromothersources)areaddedtothechanneloutput,withtheresultthatthereceivedsignalisacorruptedversionofthetransmittedsignal.

(2)

Aquantitativewaytoaccountfortheeffectofnoiseistointroducesignal-to-noiseratio(SNR)asasystemparameter.Forexample,wemaydefinetheSNRatthereceiverinputastheratiooftheaveragesignalpowertotheaveragenoisepower,bothbeingmeasuredatthesamepoint.ThecustomarypracticeistoexpresstheSNRindecibels(dBs),definedas10timesthelogarithm(tobase10)ofthepowerratio.Forexample,signal-to-noiseratiosof10,100and1,000correspondto10,20,and30dBs,respectively.

(3)

Thesecondsourceofinformation,music,originatesfrominstrumentssuchasthepiano,violin,andflute.Thenotemadebyamusicalinstrumentmaylastforashorttimeintervalasintheprocessingofakeyonapiano,oritmaybesustainedforalongtimeintervalasintheexampleofafluteplayerholdingaprolongednote.Typically,musichastwostructures:amelodicstructureconsistingofasetofsimultaneoussounds.Likeaspeechsignal,amusicalsignalisbipolar.However,amusicalsignaldiffersfromaspeechsignalinthatitsspectrumoccupiesamuchwiderbandoffrequenciesthatmayextenduptoabout15kHz.Accordingly,musicalsignalsdemandamuchwiderchannelbandwidththanspeechsignalsfortheirtransmission.

參考譯文

第一單元通信過程

今天，通信以許多不同的方式進(jìn)入到了我們的日常生活，以至于可以很容易地忽視它的許多方面。我們手中的電話、客廳里的收音機(jī)和電視、辦公室和家里接入到互聯(lián)網(wǎng)的計(jì)算機(jī)終端以及報(bào)紙都能夠從地球的每個(gè)角落(為我們)提供快速的通信。通信為公海上的船只、飛行中的飛行器、空中的火箭和衛(wèi)星提供了感知能力。通過無線電話可使汽車駕駛員與幾英里外的辦公室或家人保持通信聯(lián)系。通信可使天氣預(yù)報(bào)人員通過多個(gè)傳感器獲得天氣情況。通信的方式各種各樣，通信應(yīng)用的例子幾乎不勝枚舉。最基本的，通信無疑涉及了信息通過一系列的過程從一個(gè)點(diǎn)到另一個(gè)點(diǎn)的傳輸，其過程描述如下：

(1)信息的產(chǎn)生：話音、音樂、圖片或計(jì)算機(jī)數(shù)據(jù)。

(2)通過一系列的符號(hào)——電的、聽覺的或視覺的方式，使用一定的測(cè)量精度對(duì)信息符號(hào)進(jìn)行描述。

(3)以適合物理介質(zhì)傳輸?shù)男问綄?duì)這些符號(hào)進(jìn)行編碼。

(4)把編碼后的符號(hào)傳輸?shù)狡谕哪康牡亍?/p>

(5)原始符號(hào)的解碼和再現(xiàn)。

(6)原始信息信號(hào)的再生，這種再生信號(hào)的質(zhì)量下降是可界定的，是由系統(tǒng)的非理想性引起的。

當(dāng)然，還有很多種通信形式不需要人的頭腦的實(shí)時(shí)參與。例如，在計(jì)算機(jī)通信中兩個(gè)或多個(gè)計(jì)算機(jī)通信時(shí)，人類的決定只是在安裝程序或?qū)﹄娔X發(fā)出命令或監(jiān)視結(jié)果時(shí)才參與到通信過程中。

不考慮正在討論的通信過程的形式，每一個(gè)通信系統(tǒng)都有三個(gè)基本元素，即發(fā)射器、信道和接收器，如圖1.1所示。發(fā)射器在空間上位于通信的一端，接收器位于和發(fā)射器分開的另一端，信道是連接發(fā)射器和接收器的物理介質(zhì)。發(fā)射器的目的是把信源產(chǎn)生的信息轉(zhuǎn)換為適合信道傳輸?shù)男盘?hào)形式。但是，隨著在信道中的傳播，被傳輸?shù)男盘?hào)會(huì)因信道的非理想性而失真。而且，噪聲和干擾信號(hào)(來自于其他信源)會(huì)疊加在信道輸出端，結(jié)果使得接收到的信號(hào)是惡化后的傳輸信號(hào)。接收器的任務(wù)是對(duì)接收到的信號(hào)進(jìn)行重建，使其成為用戶能辨識(shí)的原始信息信號(hào)的形式。

圖1.1通信系統(tǒng)的構(gòu)成通信有兩種基本的模式：

(1)廣播方式。這種方式使用一個(gè)大功率的發(fā)射器和多個(gè)接收器，(這里的)接收器的制造是相對(duì)廉價(jià)的。這里承載信息的信號(hào)只向一個(gè)方向傳輸。

(2)點(diǎn)對(duì)點(diǎn)通信。在這種方式中，通信過程在單個(gè)發(fā)射器和接收器之間的鏈路上發(fā)生。在這種情況下，承載信息的信號(hào)通常是雙向傳輸?shù)?，這需要使用鏈路兩端的發(fā)射器和接收器。收音機(jī)和電視是廣播通信方式的例子，普遍使用的電話提供了一種點(diǎn)對(duì)點(diǎn)通信的手段。

所有這些不同的通信過程以及此處未提及的通信過程都有一個(gè)共同的特點(diǎn)：在本質(zhì)上，潛在的通信過程都是(遵循)統(tǒng)計(jì)學(xué)(特征)的。實(shí)際上，正是由于這個(gè)重要原因，本書的大部分內(nèi)容都致力于(闡述)通信系統(tǒng)的統(tǒng)計(jì)學(xué)基礎(chǔ)。

1．主要的通信資源

在通信系統(tǒng)中，使用了兩種主要的資源：傳輸功率和信道帶寬。傳輸功率是傳輸信號(hào)的平均功率。信道帶寬定義為分配給信息信號(hào)傳輸用的頻帶。一般系統(tǒng)的設(shè)計(jì)目標(biāo)是盡量高效地利用這兩種資源。在大多數(shù)通信信道中，一種資源可能會(huì)被認(rèn)為比另一種資源更重要。因此，我們可以把通信信道分為功率受限或波段受限兩種。比如，電話電路是典型的波段受限信道，而空間通信鏈路或衛(wèi)星信道是典型的功率受限信道。當(dāng)信息信號(hào)的頻譜向下擴(kuò)展到低頻或0時(shí)，我們把信號(hào)帶寬定義為上限頻率，高于上限頻率的信號(hào)頻譜分量可以忽略，因此對(duì)于信息的傳輸也是不必要的。舉例來說，普通話音頻譜可以適當(dāng)?shù)財(cái)U(kuò)展到10

kHz以外，盡管大部分的平均功率集中在100

Hz～600

Hz之間，但是300

Hz～3100

Hz的波段就可以提供良好的話音清晰度。因此，我們發(fā)現(xiàn)電話電路對(duì)300

Hz～3100

Hz頻率范圍響應(yīng)良好，能夠提供十分滿意的商業(yè)電話業(yè)務(wù)。我們必須牢記的另一個(gè)要點(diǎn)是：通信系統(tǒng)中不可避免地存在著噪聲。噪聲指的是通信系統(tǒng)中可能干擾信息信號(hào)傳輸和處理的多余波。噪聲可來源于系統(tǒng)內(nèi)部或外部。

對(duì)噪聲的影響進(jìn)行定量分析的方法是引入信噪比(SNR)作為系統(tǒng)參數(shù)。舉例來說，我們可以在接收器輸入端把SNR定義為同點(diǎn)測(cè)量的平均信號(hào)功率與平均噪聲功率的比值。習(xí)慣的做法是用分貝(dB)來表示SNR，分貝定義為功率比值的對(duì)數(shù)(以10為底)的10倍。比如，信噪比為10、100和1000時(shí)，系統(tǒng)的分貝數(shù)分別為10

dB、20

dB和30

dB。

2．信息源

電信環(huán)境是由四個(gè)重要的信息源決定的：話音、音樂、圖片和計(jì)算機(jī)數(shù)據(jù)。信息源的特性可以用攜帶信息的信號(hào)來定義。信號(hào)定義為時(shí)間的單值函數(shù)，時(shí)間是自變量；在每一個(gè)時(shí)刻函數(shù)有一個(gè)唯一的值。信號(hào)可以是一維的，如話音、音樂或計(jì)算機(jī)數(shù)據(jù)。圖片信號(hào)是二維的；視頻數(shù)據(jù)信號(hào)是三維的；隨時(shí)間變化的大量數(shù)據(jù)是四維的。接下來，我們?cè)敿?xì)說明不同的信息來源。

(1)話音是人類交流的基本手段。特別地，話音交流過程包含從說者到聽者的信息的傳輸，具體包括三個(gè)連續(xù)的階段：

①話音產(chǎn)生階段。說話者頭腦中的想法由包含了聲音(即壓力波)的話音信號(hào)表達(dá)出來，這些聲音由聲道產(chǎn)生，其排列組合受控于語言規(guī)則。

②傳輸階段。聲波以300m/s的速度在空氣中傳播，到達(dá)聽者的耳朵。

③理解階段。接收的聲音由收聽者解釋成接收信息，通過完成一連串的事件，最終實(shí)現(xiàn)信息從說者到聽者的傳送。話音產(chǎn)生過程可以看做一種過濾形式，在此過程中，聲源激勵(lì)聲道過濾器。聲道包括一個(gè)截面不均勻的管道，開始于聲門(即聲帶間的開口)，終止于嘴唇。當(dāng)聲音沿著聲道傳播時(shí)，頻譜(即頻率分量)會(huì)受到聲道頻率選擇的整形，這種作用有些類似于風(fēng)琴管道的共鳴。這里要重點(diǎn)提及的是話音的功率譜(即長(zhǎng)期平均功率隨頻率的分布)在0頻率附近逼近0，而在數(shù)百赫茲頻率附近達(dá)到峰值。但是，為了對(duì)事物進(jìn)行正確的觀察，我們必須牢記聽力機(jī)制對(duì)頻率是非常敏感的。而且，通信系統(tǒng)類型對(duì)頻率的波段有重要的影響，而頻率對(duì)通信過程是必不可少的。比如，就像前面提到的，300

Hz～3100

Hz的帶寬對(duì)于商業(yè)電話通信是能夠滿足需要的。

(2)第二個(gè)信源是音樂，它是由樂器，比如鋼琴、小提琴和長(zhǎng)笛發(fā)出的。樂器發(fā)出的音可能持續(xù)一個(gè)短的時(shí)間，如敲擊一個(gè)鋼琴鍵，或可以持續(xù)一個(gè)長(zhǎng)的時(shí)間，如長(zhǎng)笛演奏者吹出的長(zhǎng)音。典型地，樂聲有兩個(gè)結(jié)構(gòu)：一個(gè)旋律結(jié)構(gòu)包含了一系列同時(shí)發(fā)出的聲音。類似話音信號(hào)，音樂是雙極性信號(hào)。但是，音樂信號(hào)不同于話音信號(hào)，因?yàn)樗念l譜占據(jù)了更寬的頻率波段，此頻率可擴(kuò)展到大約15kHz。因此，音樂信號(hào)的傳輸需要比話音信號(hào)更寬的信道帶寬。

EXTENSIVETEXT

Shannon’sInformationCapacityTheorem

Thegoalofacommunicationsystemdesigneristoconfigureasystemthattransportsamessagesignalfromasourceofinterestacrossanoisychanneltoauserattheotherendofthechannelwiththefollowingobjective:

Themessagesignalisdeliveredtotheuserbothefficientlyandreliably,subjecttocertaindesignconstraints:allowabletransmitpower,availablechannelbandwidth,andaffordablecostofbuildingthesystem.

Inthecaseofadigitalcommunicationsystem,reliabilityiscommonlyexpressedintermsofbiterrorrate(BER)orprobabilityofbiterrormeasuredatthereceiveroutput.Clearly,thesmallertheBER,themorereliablethecommunicationsystemis.AquestionthatcomestomindinthiscontextiswhetheritispossibletodesignacommunicationsystemthatoperateswithzeroBEReventhroughthechannelisnoisy.Inanidealsetting,theanswertothisquestionisanemphaticyes.TheanswerisembodiedinoneofShannon’scelebratedtheorems,whichiscalledtheinformationcapacitytheorem.

LetBdenotethechannelbandwidth,andletSNRdenotethereceivedsignal-to-noiseratio.Theinformationcapacitytheoremstatesthatideallythesetwoparametersarerelatedas

C

=

Blb(1

+

SNR)b/s(1)

WhereCistheinformationcapacityofthechannel.Theinformationcapacityisdefinedasthemaximumrateatwhichinformationcanbetransmittedacrossthechannelwithouterror;itismeasuredinbitspersecond

(b/s).ForaprescribedchannelbandwidthBandreceivedSNR,theinformationcapacitytheoremtellsusthatamessagesignalcanbetransmittedthroughthesystemwithouterrorevenwhenthechannelisnoisy,providedthattheactualsignalingrateRinbitspersecond,atwhichdataaretransmittedthroughthechannel,islessthantheinformationcapacityC.

Unfortunately,Shannon’sinformationcapacitytheoremdoesnottellushowtodesignthesystem.Nevertheless,fromadesignpointofview,thetheoremisveryvaluableforthefollowingreasons:

(i)

TheinformationcapacitytheoremprovidesaboundonwhatrateofdatatransmissionistheoreticallyattainableforprescribedvaluesofchannelbandwidthBandreceivedSNR.Onthisbasis,wemayusetheratio

asameasureoftheefficiencyofthedigitalcommunicationsystemunderstudy.Thecloserηistounity,the

moreefficientthesystemis.

(ii)

Equation(1)providesabasisforthetrade-offbetweenchannelbandwidthBandreceivedSNR.Inparticular,foraprescribedsignalingrateR,wemayreducetherequiredSNRbyincreasingthechannelbandwidthB,hencethemotivationforusingawidebandmodulatedscheme(e.g.pulse-codemodulation)forimprovednoiseperformance.

(iii)

Equation(1)providesanidealizedframeworkforcomparingthenoiseperformanceofonemodulationschemeagainstanother.

ADigitalCommunicationProblem

Whenwespeakofadigitalcommunicationsystemhavingalowbiterrorrate,say,theimplicationisthatonlyasmallfractioninalongstreamofbinarysymbolsisdecodedinerrorbythereceiver.Theissueofthereceiverdeterminingwhetherabinarysymbolsentoveranoisychannelisdecodedinerrorornotisoffundamentalimportancetothedesignofdigitalcommunicationsystems.Itisthereforeappropriatebrieflytodiscussthisbasicissuesoastomotivatethestudyofcommunicationsystems.

Supposewehavearandombinarysignal,m(t),consistingofsymbols1