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1、第二章第一篇To say that we live in an age of electronics is an understatement。From the omnipresentintegrated circuit to the equally omnipresent digital computer,we encounter electronic devices andsystems on a daily basis。In every aspect of our increasingly technological society whether it isscience,engine
2、ering,medicine，music,maintenance，or even espionagethe role of electronicsis large，and it is growing.谈论关于我们生活在一个电子学时代的论调是一种空泛的论调.从无处不在的集成电路到同样无处不在的数字计算机，我们在日常活动中总会遇到电子设备和电子系统。在我们日益发展的科技社会的方方面面无论是在科学、工程、医药、音乐、维修方面甚至是在谍报方面-电子学的作用是巨大的，而且还将不断增强。In general，all of the tasks with which we shall be concerned
3、 can be classifiedassignal-processing“tasks。Let us explore the meaning of this term一般说来，我们将要涉及到的工作被归结为“信号处理”工作，让我们来探究这个术语的含义吧.A signal is any physical variable whose magnitude or variation with time contains information.This information might involve speech and music,as in radio broadcasting，a physi
4、cal quantitysuch as the temperature of the air in a room，or numerical data,such as the record of stock markettransactions。The physical variables that can carry information in an electrical system are voltageand current。When we speak of signals”,therefore,we refer implicitly to voltages or currents.H
5、owever，most of the concepts we discuss can be applied directly to systems with differentinformationcarrying variables.Thus，the behavior of a mechanical system(in which force andvelocity are the variables）or a hydraulic system（in which pressure and flow rate are thevariables)can often be modeled or r
6、epresented by an equivalent electrical system.Anunderstanding of the behavior of electrical systems，therefore,provides a basis for understandinga much broader range of phenomena。信号就是其与时间有关的量值或变化包含信息的任何物理变量。这种信息或许像无线电广播的演讲和音乐，或许是像室内温度的物理量，或许像股市交易记录的数字数据。在电气系统中能够载有信息的物理变量是电压和电流。因此当我们谈到“信号”，我们不言而喻指的是电压
7、和电流，然而,我们要讨论的大多数概念是可以被直接应用于载有不同信息的变量的系统，因此，一个机械系统（在这个系统中力和速度是其变量）或者液压系统（在这个系统中压力和流速是其变量）的性能通常可以用一个等效的电气系统来模拟或表示。因此,我们对于电气系统性能的理解为理解更宽领域的现象打下了一个基础.A signal can carry information in two different forms.In an analog signal the continuous variationof the voltage or current with time carries the informat
8、ion.An example,in Fig.2l，is thevoltage produced by a thermocouple pair when the two junctions are at different temperatures.Asthe temperature difference between the two junctions varies,the magnitude of the voltage acrossthe thermocouple pair also varies.The voltage thus provides an analog represent
9、ation of thetemperature difference。一个信号可以以两种形式来承载信息。在一个模拟信号中电压或电流随时间而产生的连续变化载有信息。在图 2-1 中，当一对热电偶的接头处于不同的温度时由热电偶所产生的电压就是一个例子.当两个接头之间的温度差改变时，一对热电偶两端的电压也将改变。于是电压就提供了温度差的模拟表现形式The other kind of signal is a digital signal.A digital signal is one that can take on values withintwo discrete ranges.Such sign
10、als are used to represent ON-OFF or YESNO information.An1ordinary householdthermostatdeliversadigitalsignaltocontrol the furnace.When theroom temperature drops below a preset value，the thermostat switch closes turning on thefurnace。Once the room temperature rises high enough，the switch opens turning
11、 off the furnace.The current through the switch provides a digital representation of the temperature variation:ONequals”too cold”while OFF equals not too cold.另一种的信号是数字信号.数字信号是在两个离散的范围内能够呈现一定数值的信号。这种信号常用以表示“开关或“是-不是信息。一个普通的家用恒温器传递一种数字信号来控制炉子当房间的温度下降到预定温度以下时，恒温器的开关合上使炉子开始加热;一旦房间的温度上升到足够高,开关就断开使炉子关闭.流
12、过开关的电流提供了温度变化的数字表示：ON即为“太冷而 OFF 即为“不太冷A signal-processing system is an interconnection of components and devices thatcan accept aninput signal or a group of input signals,operate on the signals in some fashion either to extract orimprove the quality of the information,and present the information as
13、an output in the proper format the proper time.一个信号处理系统是某些元件或设备之间的相互连接,这些元件和设备能够接收一个输入信号或一组输入信号，信号处理系统以某种方式来处理这些信号即提取这些信号或提高这些信号的品质，然后在适当的时间以适当的形式把这个信号表示为输出量。Fig.2-2 illustrates the components in such a system。The central circles represent the two types ofsignal processing(digital and analog），whilet
14、heblock between the two signal processingblocksrepresentstheconversionofananalogsignaltoequivalentdigitalform（A/D=AnalogtoDigital）and the reverse conversion of a digital signal to the correspondinganalog form（D/A=DigitaltoAnalog)。The remaining blocks involve inputs and outputsgetting signals into an
15、d out of the processing system。图 22 显示了这样一个系统的组成部分.中间的圆圈代表了两种类型的信号处理（数字和模拟），而处于信号处理框之间的方框表示模拟信号向等效数字形式（A/D 即模拟到数字）的转换，以及从数字信号向相应的模拟形式(D/A 即数字到模拟）的逆转换。剩下的方框涉及输入和输出-取得信号以及从处理系统输出信号。Many electrical signals derived from physical systems are obtained from devices calledtransducers。We have already encount
16、ered an example of an analog transducer，thethermocouple pair.It converts temperature difference（the physical variable）to a voltage(theelectrical variable)。Generally,a transducer is a device that converts a physical or mechanicalvariable to an equivalent voltage or current signal.Unlike the thermocou
17、ple example,however，most transducers require some form of electrical excitation to operate从物理系统获得的很多电气信号是从被称为传感器的器件中输入的。我们已经碰到了一个模拟传感器的例子。即热电偶。它把温度的变化（物理变量)转换成电压（电气变量)。通常，传感器是一种将物理或机械变量转换成等效电压或电流信号的器件.然而,不同于热电偶例子，大多数传感器需要一些形式的电激励以驱动传感器The output from a system can be in many forms，depending on the us
18、e to be made of theinformation contained in the input signals。One can seek to display the information，either inanalog form（using a meter，for example,in which the needle position indicates the size of thevariable of interest)or in digital form（using a set of digital display elements that are lit up w
19、ith anumber corresponding to the variable of interest）。Other possibilities are to convert the output tosound energy（with a loudspeaker），or to use the output asan input signal to another system，or to use the output as a control signal to initiate some action。2个系统的输出可以有多种形式，这取决于包含在输入信号中的信息所起的作用。我们可以选择
20、何种方式显示这些信息，无论是以模拟形式（例如,使用一种仪表,仪表的指针的位置指明我们所感兴趣的变量的大小)或是以数字形式(使用一套数字显示元件，显示对应于我们所感兴趣的变量的数字)。其它的可能的情况下是将输出转换成声能（利用扬声器），或是将输出作为另一个系统的输入，或是利用输出作为控制信号来产生某个动作第二篇The mathematics of computers and other digital electronic devices have been developed from thedecisive work of George Boole（l815l864)and many oth
21、ers，who expanded and improved onhis work.The body of thought that is known collectively as symbolic logic established theprinciples for deriving mathematical proofs and singularly modified our understanding and thescope of mathematics.布尔代数也称为逻辑代数。它是英国数学家乔治布尔(18151864）于1849 年创立的。在当时，这种代数纯粹是一种数学游戏。在布尔
22、代数里，布尔构思出一种关于0 和 1 的代数系数，用基础的逻辑符号系统描述物体和概念。这种代数不仅广泛于概率和统计等领域，更为重要的是,它为数字计算机开关电路设计提供了最重要的数学方法。Only a portion of this powerful system is required for our use.Boole and others were interested indeveloping a systematic means of deciding whether a proposition in logic or mathematics was trueor false,but
23、we shall be concerned only with the validity of the output of digital devices.True andfalse can be equated with one and zero,high and low,or on and off。These are the only two statesof electrical voltage from a digital element。Thus，in this remarkable algebra performed by logicgates,thereareonlytwoval
24、ues,oneandzero；anyalgebraic combination ormanipulation can yield only these two values.Zero and one are the only symbols in binaryarithmetic这种很有用的系统中只有一部分内容为我们所应用.布尔等人感兴趣的是推导出一种用来判断某个命题在逻辑上或在数学上是真还是假的系统性的方法,但我们要关注的仅仅是数字设备的输出的正确与否。真或假可以等同于一和零，或者等同于开和关。这是电子元件中电压的两种唯一的状态.因此，由逻辑门所完成的这个奇异的代数中,只有两种值，一和零,任
25、何代数组合或者计算只能产生这两种值。零和一是二进制运算中唯一的符号The various logic gates and their interconnections can be made to perform all the essentialfunctions required for computing and decisionmaking.In developing digital systems the easiestprocedure is to put together conceptually the gates and connections to perform the
26、assigned task inthe most direct way.Boolean algebra is then used to reducethe complexityofthesystem，ifpossibl，ewhile retaining the same function.The equivalent simplified combination of gateswill probably be much less expensive and less difficult to assemble 不同的逻辑门和它们之间的相互连接可以用来完成计算以及判断所要求的必要的功能。在开发
27、数字系统时最简单的做法是把逻辑门以及它们之间的连接根据概念排放在一起 以最直接的方式完成 设定的任务.于是我们采用布尔代数来减小系统的复杂程度，如果可能的话，与此同时应保留其相同的功能。逻辑门之间等效的简单的组合可能使得费用更加便宜而在装配上更加容易。Boolean algebra has three rules of combination,as any algebra must have:the associative,thecommutative，and the distributive rules。To show the features of the algebra we use t
28、he variablesA，B,C,and so on。To write relations between variables each one of which may take the value0 or l，we usetomean“not A,”so ifA=l,then=0.Thecomplement ofevery variable is expressed by placing a bar over the variable;thecomplement of=”not B”。Two fixed quantities also exist.The first is identit
29、y，I I=l;the other is null，3null=0布尔代数与任何代数一样具有结合律、交换律和分配律。为了表示代数的特性我们使用变量A,B 和 C 以及诸如此类的变量。为了写出这些可能取值为 0 或 1 的各个变量之间的相互关系，我们采用来表示“非 A”，因此如果A1，那么0。每个变量的补码用每个变量上方加一横线来表示，B 的补码就是也即“非 B”。同时还存在两个固定的量.第一个量是单位量，即 I1，另外一个量是零，即 null0。Boolean algebra applies to the arithmetic of three basic types of gates:an
30、OR-gate，an AND-gateand the inverter.The symbol and the truth tables for the logic gates are shown in Fig。2-3，thetruth table illustrate that the AND-gate corresponds to multiplication,the ORgate corresponds toaddition,and the inverter yield the complement of its input variable。布尔代数应用于三种基本类型的逻辑门的运算：一种
31、是或门，一种是与门，还有一种是反相器（非门）.逻辑门的符号和真值表如图23 所示，真值表显示与门对应于乘，或门对应于加,而反相器产生其输入变量的补码We have already found thatAB=A AND Bfor the ANDgate andA+B=A OR Bfor the ORgate 我们已经算出对于与门来说AB=“A AND B而对与或门来说 A+B=“AOR B”The AND，or conjunctive,algebraic form and the OR，or disjunctive,algebraic form must eachobey the three r
32、ules of algebraic combination。In the equations that follow，the reader may usethe two possible values 0 and l for the variables A,B，and Cto verify the correctness of eachexpression。Use A=0,B=0,C=0；A=l,B=0，C=0；and so on，in each expression.The associative rules state how variables may be grouped。对于“与”，
33、即逻辑乘,以及“或”，即析取，它们的代数形式必须遵循代数组合的三个法则。在接下来的等式中,读者可以把变量 A，B,C 设为两个可能的值 0 和 1 来证明每个表达式的正确性。例如采用 A=0,B=0,C=0，或 A=1,B=0,C=0 等等，在每个表达式中，结合律表明如何把变量进行重组ForAND（AB）C=A(BC)=（AC）B,and forOR（A+B）+C=A+(B+C）=（A+C）+B对于“与有（AB）CA（BC）（AC）B 而对于“或”有(AB)CA（BC)(AC）Bthe rules indicate that different groupings of variables m
34、ay be used without altering the validity ofthe algebraic expression 这个法则表明我们可以采用变量的不同组合而不改变代数表达式的正确性。交换率表明了变量的顺序The commutative rules state the order of variables.ForANDAB=BAand forORA+B=B+Athe rules indicate that the operations can be grouped and expanded as shown对于“与”有 ABBA，而对于“或”有 ABBA.这个法则表明了可以如
35、上式所示进行运算的组合和展开Before we show the remaining rules of Boolean algebra for digital devices，let us confirm thedistributive rule for AND by writing the truth table，Table 2-l。We will discover soon how weknew that we could write AB+C=(A+C)(B+C），which is proved by the truth table to be aproper expansion.在我们
36、展示数字设备布尔代数的剩下的那个法则之前，让我们通过写出真值表的方式即真值表 21 来验证对于“与”的分配律。我们将很快发现如何写出等式ABC（AC)(BC),这一等式由真值表证明了是一个正确的展开式。4The more complex expression and its simpler form yield identical values。Because binary logic isdominated by an algebra in which a sum of ones equals one，the truth table permits us to identifythe equ
37、ivalence among algebraic expressions。A truth table may be used to find a simplerequivalent to a more complex relation among variables，if such an equivalent exists。We will seeshortly how the reduction of complexity may be achieved in a systematic manner with truth tablesand other techniques 更为复杂的表达式和
38、它的一次式产生了相等的值。由于二进制逻辑取决于某一代数,其单个变量之和等于一个变量，所以真值表允许我们在代数表达式中找出等效值,我们可以使用真值表来求出一个等效于变量之间较复杂的关系式的一次表达式。如果这样的等效关系存在，我们将很快看到利用真值表以及其它方法以一种系统性的方式如何完成这样一个复杂步骤的简化工作。Some additional relations in the algebra,which use identity and null，are worth nothing。Herewe illustrate properties of the AND and OR operations
39、 that use the distributive rules and the factthat I is always l and null is always 0。ANDAI=AorA1=AORA+null=AA+0=AANDA=nullA=0ORA+=IA+=1ANDA null=nullA0=0ORA+I=IA+1=1ANDAA=AORA+A=AThe relationpoints out an important fact,that is，that I,the identity,is theuniversal set。Null is called the empty set。代数中
40、另外的一些关系式，这些式子中使用单位一和零，是没有意义的,这里我们列举了运用分配律后“与”和“或”运算的性质，结果是 1 永远是 1 而零永远是 0。与：AIA 即 A1A或:AnullA 即 A0A与：即或：即与:Anull0 即 A00或：AII 即 A11与：AAA或:AAA关系式 AAI 指出了一个重要事实，即I，也就是单位量，是全集,而零被称为空集。We have considered several logical relations.For the twovalue Boolean algebra of digitalelectronics，the choice of the t
41、echnique depends upon the nature of the function whose reductionis desired.Some simple functions may be easily reduced by examining their truth table；othersrequire the manipulation of Boolean algebra to reveal the relationship。Whenweconsiderthecircuitforadding binary numbers，we see that Boolean algebra is required to discover asimplification in that particular application 我们已经研究了几种逻辑关系。对于电子学的二值布尔代数来说,选择何种方法取决于我们所期望的简化函数的性质。一些简单的函数可以通过观察它们的真值表很容易进行简化；而另一些函数需要通过计算布尔代数来揭示它们的关系。当我们研究有关二进制数相加的电路时，我们将看到需要布尔代数来揭示该特定应用中的简化过程5