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1、 Lession 1Function in use normal probability function 概率正态分布函数 orthonormal function 正交函数 self-correlation function 自相关函数 trigonometrical function 三角函数 unbounded function 无界函数 unit step function 单位阶跃函数 zero Bessel function 零次贝塞尔函数 function of first degree 一次函数 function of many variables 多元函数 function
2、 of random variable 随机变量函数Periodic signals 周期信号Time-domain description 时域描述Polynomial expansion 多项式Taylor series 泰勒级数Fourier series 傅里叶级数Frequency-domain description 频域描述Orthogonal function 正交函数Vectors 矢量Description in dictionary 描述:描述的行为,过程或技术 声明,叙述:描述某事的声明或叙述 用画表示: 一种,一类:Description in text A disc
3、ussion of orthogonal functions and of their value for the description of signals may be conveniently introduced by considering the analogy between signals and vectors. 通过分析信号和矢量之间的相似之处,引入用来描述信号的正交函数概念。 Description in use published a description of her travels; gave a vivid description of the game 出版
4、她的游记;关于这场比赛的生动描述 Monets ethereal descriptions of haystacks and water lilies. 莫内关于干干草垛和睡莲的精妙描绘 cars of every size and description. 各种大小和类型的小汽车Function in dictionary 作用,功能 职务,职责 角色,工作 重大聚会,庆典 函数:功能 : 操作:子程序 Function in text The fact that great majority of functions which may usefully be considered as
5、signals are functions of lends justification to the treatment of signal theory in terms of time and of frequency. 借助于时间和频率的信号处理理论,许多常被看作是信号的函数都用来进行信号处理。 Involve in dictionary 含有,包括:包括;含有为一部分 伴随,连同:作为必需特色和影响而拥有;伴随 使牵涉,卷入:使某人卷进来;使参与 密切关联,牵连:和直接有关,经常指使某人担上罪责;牵连: 影响:影响或对产生作用: 具有或吸引的兴趣: 复杂:使错综复杂;把复杂化 包围;
6、裹住:围绕或缠绕Involve in text A complete time-domain description of such a signal involves specifying its value precise at every instant of time. 周期信号的完整的时域描述包括详细指明其在每个瞬间的精确值。 Involve in use was told that the job would involve travel See Synonyms at include 被告知那份工作将需要出差参见 include involved the bystanders i
7、n his dispute with the police. 把旁观者牵扯进他与警察的争执 evidence that involved the governor in the scandal. 州长牵连进丑闻的证据 The matter is serious because it involves your reputation. 这件事很严重,因为它影响到你的声誉 a story that completely involved me for the rest of the evening. 一个让我在那天晚上余下的时间完全沉浸其中的故事component in dictionary 成分
8、,系统的组成要素,零件component in text There are a number of reasons why signal representation in terms of a set of component sinusoidal waves occupies such a central role in signal analysis. 有许多理由可以说明为什么在信号分析时信号成份中正弦波起到如此重要的作用。 component in use One of the essential, functioning parts of a subsystem or equipm
9、ent, possibly a self-contained element, or a combination of parts, assemblies, attachments, or accessories.子系统或设备的基本组成部分或功能部件之中的一个。它可以是一种独立的元件,也可以是若干部件、装配件或附件的组合。 In software engineering, a basic part of a system or program. For example, the scheduler or supervisor of an operating system.在软件工程中,系统或程
10、序的基本部分。例如, 操作系统中的调度程序或管理程序。component in use chrominance signal component彩色色度信号分量 circuit component电路元件1)The theoretical treatment of periodic waveforms assumes that this exact repetition is extended throughout all time, both past and future.周期波形的理论假定这种精确的重复延伸到整个时间轴上,不管过去还是未来。2)Generally speaking, th
11、e fit to the actual waveform is good in the region of the point chosen, but rapidly deteriorates to the either side.一般来说,在选定点的区间内,级数与实际波形很吻合,但是在区间外,这种情况就会迅速恶化。3)its value precise at every instant of time每个瞬间的精确值 4)as number of polynomial terms 随着多项式幂的加大 5)There are a number of reasons why signal rep
12、resentation in terms of a set of component sinusoidal waves occupies such a central role in signal analysis.有许多理由可以说明为什么在信号分析时信号成分中正弦波起到如此重要的作用。 6)to be minimized in a certain important sense降到最低 7)A large and extremely important class of electrical and mechanical systems, known as linear systems, r
13、esponds sinusoidally when driven by a sinusoidal disturbing function of any frequency.一个庞大的而且极其重要的机电系统,也称作线性系统,加上任何频率的正弦干扰后都会得到正弦响应。 8)A vector is specified both by its magnitude and direction, familiar examples being force and velocity.矢量用大小和方向来描述,例如力和速度。 9)Signal description by sets of orthogonal
14、function利用正交函数集描述信号10)Suppose that we have approximated a signal over a certain interval by the function so that the mean square error is minimized.假定我们在一定区间上通过函数已经得到一个近似的信号,并且均方差达到最小。Excises 简谐信号是最简单和最重要的周期信号。任意一个周期信号可以用简谐信号来表达,两者之间联系的桥梁是傅立叶级数,所以傅立叶级数是周期信号分析的理论基础。 Harmonic signal is the simplest an
15、d the most important periodic signal. Harmonic signal can be arbitrarily used to express a periodic signal and Fourier series is a relating bridge between them, so Fourier series is the theoretical foundation of analyzing periodic signal. 一个在时域上显得很复杂的信号,将其变换或映射到频域(包括s和z域),就能够分解为非常简单的基本信号形式,进行分析和求解。
16、One signal which is a very complicated signal in the time domain is transformed or mapped o to the frequency domain (including s and z domain), it can be decomposed into very simple forms of the basic signal for analysis and solution. 3、频谱是由不连续的谱线组成,每条谱线代表一个谐波分量。这种频谱称为离散频谱。谱线之间的间隔等于基波频率的整数倍。即频谱中的每一条
17、谱线只能出现在基波频率的整数倍上,各谐波的频率都是基波频率的整数倍。 The spectrum is composed of discontinuous lines and each line is a representative of each harmonic component. This spectrum is called discrete spectrum. The interval between the lines is equal to integral times of the fundamental frequency. Each line of the spectru
18、m appears in integral times of the fundamental frequency, the frequency of the harmonics are integral times of fundamental frequency.4.The Fourier series is a particular type of orthogonal series representation that is very useful in solving engineering problems, especial communication problems. The
19、 orthogonal functions that are either sinusoids, or, equivalently, complex exponential functions.傅立叶级数是一个特定类型的正交级数的表达式,这在解决工程问题是非常有用的,尤其是通信问题。正交函数要么是正弦曲线,或等效为复指数函数。5.For periodic waveforms, the Fourier series representations are valid over all time. Consequently, the (two-side) spectrum, which depen
20、ds on the waveshape from to , may be evaluated in terms of Fourier coefficients.对于周期波形,傅立叶级数表示在整个时间轴上是有效的。因此,取决于从 到区间的波形(两方)的频谱可根据傅里叶系数来计算。In the operation of a sonar system the operator is repeatedly faced with the problem of detecting a signal which is obscured by noise. This signal may be an echo
21、 resulting from a transmitted signal over which the operator has some control, or it may have the origin in some external source. These two modes of operation are commonly distinguished as active and passive sonar, respectively. Similar situations arise in radar surveillance and in disciplines for t
22、echniques and for illustrations of the basic principles.在运作的声纳系统时,操作员一再面临的问题是如何探测噪声掩盖的信号。这一信号可能是源自于操作员控制的某些传输信号的回波,或者它有可能起源于一些外部源。这两种运作方式经常被分别作为主动和被动声纳。类似的情况出现在雷达监视以及学科技术和基本原理说明。Frequently it is desirable to determine not only the presence or absence of the signal but also one or more parameters ass
23、ociated with the signal. The parameters of interest can vary widely from a simple quantity such as time of arrival or target bearing to the recovery of the complete waveform. When a system is designed to recover one or more parameters associated with the signal, one speaks of signal extraction.经常需要确
24、定的不仅是信号的存在与否,而且是与信号相关的一个或多个参数。需要注意的参数可以有很大的不同,从一个简单的量,如到达时间或目标方位,到完整波形的恢复。当一个系统是为了恢复与信号相关的一个或多个参数,这就谈到信号提取。A final source of pulse distortion is the Doppler shifts produced by the relative motions between the source, the medium, the bottom, and the targets. Since the source, the medium, and the targ
25、et (or detector in passive listening) may each have a different vector velocity to the bottom, the variety of effects may be quite large.脉冲失真的最终原因是多普勒位移,它产生于源、介质、末端和目标之间的相对运动。既然源、媒质和目标(或被动收听的探测器)对末端有不同矢量速度,所以各种效应可能相当大。 Lession 2v Terminology The real part 实部The imaginary part 虚部Amplitude 振幅Spectrum
26、频谱The unit step function 单位阶越函数The exponentially decaying 指数衰减阶跃函数Lasplace transform 拉普拉斯变换Pole 极点Zero 零点Argand diagram 阿根图 precious in dictionaryv 昂贵的:价钱或价值很高的;值钱的v 珍贵的:受到高度评价的;珍藏的v 亲爱的;被热爱的v 矫揉造作的:矫饰地优美或过分文雅的v 十足的;纯粹的precious in textv In the previous chapter we have seen how a periodic signal may
27、be expressed as the sum of a set of sinusoidal waves which are harmonically related.v 在前一章中,我们已经看到周期信号是如何被表示成一组正弦谐波的叠加。 precious in usev precious mannerisms.v 矫揉造作的习气v a precious mess.v 一团糟appropriate in dictionaryv 拨出:拨出作特殊用途v 挪用,窃用:为自己独自占有或使用,常未经许可appropriate in textv either as a set of sine and c
28、osine waves of appropriate amplitude and frequency v 或者表达为适当振幅和频率的一组正弦和余弦波 appropriate in usev appropriating funds for education.v 拨款作教育基金v Lee appropriated my unread newspaper and never returned it.v 李擅自拿走我尚未阅读的报纸并从不归还visualize in dictionaryv 形成思维图像;设想v 使可见visualize in textv It is indeed hard to vi
29、sualize a wave such as an isolated pulse being composed of an infinite set of waves of infinitely small amplitudes .v 的确很难想象像这些单个脉冲是由无限个无穷小振幅的波组成 .visualize in usev tried to visualize the scene as it was described.v 尽力设想所描绘的场景demonstrate in dictionaryv 表明:清楚细致地显示;表明v 证实,论证:通过推理或引证说明真实性;证明v 演示,说明:通过实
30、验、例子或实际应用表明;解释并说明v 展示,示范:向可能的购买者示范(某物品的)使用demonstrate in textv It may seem strange that the pulse contains no energy at such frequencies, but it is not hard to demonstrate. v 似乎很奇怪,脉冲在这样的频率下没有能量,然而这是不难说明。 demonstrate in usev demonstrated her skill as a gymnast; demonstrate affection by hugging.v 显示她
31、的体操技巧;拥抱以示亲热v demonstrate a proposition.v 证明一个命题v demonstrated the laws of physics with laboratory equipment.v 用实验装置演示物理定律v The salesperson plugged in and demonstrated the vacuum cleaner.v 售货员插上电源,示范真空吸尘器的操作transform in dictionaryv 使变形:明显地改变外观或形式v 改变的性质、职能或状况v 使变换v 使(一个结构)发生转换v 变压:使经过变压器的转换v 转变:使(一个
32、细菌细胞)发生转化transform in textv So far it has been implied that the Fourier transform may be successfully used for any no-repetitive signal, but there are in fact limitations and difficulties in its applications. v 到现在为止,似乎傅立叶变换适用于任何的非重复的信号,但是事实上在它的应用中有一些限制和困难。 transform in usev A thick, fibrous fog had
33、 transformed the trees into ghosts and the streetlights into soft, haloed moonsv “浓密厚重的雾使树木看起来象鬼魂,街灯看起来象是带着柔和光晕的月亮”decay in dictionaryv 腐烂:分解成各组成部分;腐烂v 衰变:由于放射性衰变而解体或缩小v 衰减:指电压或电流的逐渐减弱v 能量衰减:指人造卫星在轨道上运行时能量消减v 衰亡,毁坏:v 使衰退:从正常、优秀或繁荣的状态衰败下去,恶化decay in textv Such terms give rise to not only the sine and
34、 cosine waves of the Fourier method, but also growing and decaying sine and cosine waves and growing and decaying exponentials.v 在大多数例子中,一个函数由许多简单的线性因子组成,部分分式法就是要我们把一个函数表示许多比较简单的函数之和,而每个简单的函数都出现在变换表中。decay in usev a civilization that had begun to decay.v 已经开始衰落的文明v It is possible to derive frequency
35、 spectra for such signals using as a starting point of the work we have already done on the Fourier series.v 我们可以通过傅立叶级数作为研究这类信号频谱的出发点。Instead of using the simple trigonometric form,we may write与下面简单三角函数表达式不同,我们可以写where m is any interger其中m 可以取任何的整数Substitution into the first equation followed by re
36、arrangement of terms yields the exponential form without difficulty.将式(23)和(24)代入式(21)并移项整理可以很容易得到指数形式的表达式。The Fourier transform (also called the Fourier integral) does for the non-repetitive signal waveform what the Fourier series does for the repetitive one.傅立叶变换(也称傅立叶积分)为非重复的信号波形分析提供了数学工具,而傅立叶级数为
37、重复的信号分析提供了数学工具。The harmonics become extremely closed spaced.它的谐波将近占满整个空间The complex coefficients are found by multiplying by and taking the average of the result over a complete period.系数 等于 与 的乘积的定积分的平均值。So we now choose to write this as a new variable .因此我们现在引出一个新的变量。returning to the first eqation
38、代到第一个方程which is now vanishingly small现在是无穷小The limits of integration are clearly reduce so that积分的上下限是有限的,有1、信号不是周期出现,而只是持续一段时间,不再重复出现,如过渡过程、爆炸产生的冲击波、起落架着陆时的信号等,把这一类信号看成为非周期信号。分析非周期信号的思路是:在时域上,当周期,周期信号变成为非周期信号;在频域上,周期信号的频谱在时的极限,变为非周期信号的频谱,即傅立叶变换。Instead of a cycle, but only for some time and no repe
39、atedly emerging, the signal can be thought as aperiodic signal, such as the transition process, the shock wave explosion, landing gear. The train of thought of analyzing aperiodic signal: in the time domain, when the cycle , the periodic signal will become aperiodic signal; In the frequency domain,
40、the periodic signal spectrum in the limit of will be aperiodic signal spectrum, namely, Fourier transform.2、信号在时域压缩倍时,则在频域中频带加宽,幅值压缩倍;反之信号在时域扩展时,在频域中将引起频带变窄,但幅值增高。When one signal is compressed times in the time domain, its band will be widen and its amplitude will be compressed times in the frequenc
41、y domain; whereas one signal is expanded in the time domain, its band will be led to become narrow and the amplitude will be increased in the frequency domain.3、It should be clear that the spectrum of a voltage (or current) waveform is obtained by a mathematical calculation and that it does not appe
42、ar physically in an actual circuit. is just a parameter (called frequency) that determines which point of the spectral function is to be evaluated.电压(或电流)波谱可由数学计算明确获得,但它在实际的物理电路中不明显。频率只是确定谱函数哪些点加以计算的一个参数。4、 One of particular interest is the consequence of working with real waveforms. In any physical
43、 circuit that can be built, the voltage (or current) waveforms are real functions (as opposed to complex functions) of time.其中尤其值得注意的是对实际波形起作用的结果。当电压(或电流)波形是时间的实函数(相对于复函数)时,任何物理电路都可建。In communication system, the received waveform is usually categorized into the desired part containing the informatio
44、n, and the extraneous or undesired part. The desired part is called the signal and the undesired part is called noise.在通信系统中,标准的波形通常分为想要且含有信息的部分以及不想要或并不相干的一部分。理想的一部分就是所谓的信号,而不受欢迎的一部分就是所谓的噪音。Physically Realizable Waveforms(可实现的物理波形) Practical waveform that are physically realizable (i.e., measurable
45、in a laboratory) satisfy several conditions: 1. The waveform has significant nonzero values over a composite time interval that is finite. 2. The spectrum of the waveform has significant values over a composite frequency interval that is finite. 3. The waveform is a continuous function of time. 4. T
46、he waveform has a finite peak value. 5. The waveform has only real values. That is, at any time, it cannot have a complex value where is nonzero. 实际的波形在物理上是可实现的,也就是说在实验室中可进行测量。它满足以下几个条件:1、 波形在一个可分解的时间区间上有非零且有限的有效值。2、 波形频谱在一个可分解的时间区间上有限的有效值3、 波形是连续的时间函数。4、 波形具有有限的峰值。波形只有实数值,也就是说,任何时间,它不能有复数值,其中,是非零值I
47、n summary, waveforms may often be classified as signals or noise, digital or analog, deterministic or nondeterministic, physically realizable or nonphysically realizable, and belonging to the power or energy type. 综上所述,波形可能常常被列为信号或噪声、数字或模拟、确定性或随意性、物理实现或非物理实现以及属于功率或能源类型。 Lesson 3 Terminology Digital
48、electronics 数字电子The Dirac function 迪拉克函数Shifting property 移位算子 Time and frequency-domain 时域和频域 Spectral lines 谱线DFT 离散傅里叶变换FFT 快速傅里叶变换Mapping 映射 Decaying oscillatory function 衰减振荡函数 underlying in dictionary 位于某物之下的: 基础的;基本的 出现但不明显的;隐含的 取得领先的;更重要的underlying in text It should be emphasized from the st
49、art that a set of sample values only forms an adequate substitute for the underlying continuous signal waveform if the interval between successive samples is sufficiently small. 必须强调的是,这一连串采样值只有当连续采样点间隔足够小时才能充分替代该连续信号波形 underlying in use underlying strata. 下层 an underlying meaning. 潜在的意义 an underlyi
50、ng financial claim. 优先的财政要求refer in dictionary 引去求助:指点到消息来源处寻求帮助或信息 归因于:指派或归因于;认为起源于 认为属于:指定或认为属于一种特定的种类或类型 遵照:提交(有争议的事件)给权威机构仲裁、决定或检查 使注意:引导的注意力:refer in text The Dirac function, often referred to as the impulse function, is a pulse of extremely short duration and unit area. 迪拉克函数,通常也叫单位脉冲函数,它是一个持续
51、时间极短且具有单位面积的脉冲。 refer in use referred her to a heart specialist; referred me to his last employer for a recommendation. 叫她找心脏病专家;叫我向他以前的雇主查询对他的推荐 refer him to his duties. 叫他把注意力放到工作上trajectory in dictionary 轨迹,弹道:抛射物或其它在空间运动的物体的运动路线 道路:选择好的或采用的路径 常角轨道,轨线:以同样的角度切割给定系统所有曲线或平面的曲线trajectory in text If w
52、e now consider values of z to be plotted on a z-plane Argand diagram, the locus of z will trace out a circle of unit radius as varies, starting on the real axis when and repeating its trajectory at intervals in of . 如果我们现在考虑在z平面的阿根图上描出z的值,z的轨迹曲线随着 的变化形成一个单位圆,这个轨迹从 时的实轴上开始,每当隔 时重复它的轨迹。 Trajectory in
53、use a moral trajectory, a style of aspiration 一条道德的道路,一种抱负的时尚reinforce in dictionary 增强:给予更多的力量或效力;加强 增援:以额外的人员或装备加强部队的力量 加强:用增加支持或物资来加强 增加:增加的数量;增加 强化刺激法:在达到需要的反应或表现后给(例如试验物)一个强化刺激的东西 强化刺激:用强化刺激的方法来刺激(一个人)reinforce in text When a large number of cosines of similar amplitude but different frequency
54、are added together, they tend to cancel each other out everywhere except at t=0, where they all reinforce. 当很多幅值相同而频率不同的余弦分量相加时,它们会在除t=0点外互相抵消,在该点它们会相互增强。 reinforce in use The news reinforced her hopes. 这个消息增强了她的希望function in dictionary 作用,功能:特别适合某人或某人所从事的行为 角色,职业:特定的工作或角色: 应变物:与另一决定它的存在、价值或重要性的事物密切
55、相关的事物: 应变量,函数:一个与他量有关联的变量,这一量中的任何一值都能在他量中找到对应的固定值function in text The Dirac function, often referred to as the impulse function, is a pulse of extremely short duration and unit area. 迪拉克函数,通常也叫单位脉冲函数,它是一个持续时间极短且具有单位面积的脉冲。 function in use in my function as chief editor. 在我担任总编辑的职位 Growth is a function of nutrition. 长身体是由营养决定的 1)One of the advantages of using the s-plane pole-zero description of a continuous signal is that it allows the spectrum to be visualized quite easily, by considering the lengths and phases of vectors drawn from the variou
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