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1、Lesson 2 Aperiodic SignalBackgroundsText tour Language in useVocabulary Structure Reading/writing techniques9/4/20241测控技术与仪器英语教程BackgroundsTerminology Fourier series 傅立叶级数 The real part 实部The imaginary part 虚部Amplitude 振幅Spectrum 频谱The unit step function 单位阶越函数The exponentially decaying 指数衰减阶跃函数Lasp
2、lace transform 拉普拉斯变换Pole 极点Zero 零点Argand diagram 阿根图 9/4/20242测控技术与仪器英语教程Text tourOutline2.1 Introduction2.2 The Exponential Form of the Fourier Series2.3 The Fourier Transform2.4 The Laplace Transform9/4/20243测控技术与仪器英语教程2.1 IntroductionThe introduction of Aperiodic signal9/4/20244测控技术与仪器英语教程2.2 Th
3、e Exponential Form of the Fourier SeriesThe Exponential Form of the Fourier Series =analysis9/4/20245测控技术与仪器英语教程2.3 The Fourier Transform2.3.1 Derivation2.3.2 Examples of Continuous Spectra2.3.3 Symmetry of the Fourier Integral Equations2.3.4 Limitations of the Fourier Transform9/4/20246测控技术与仪器英语教程2
4、.3.1 Derivationthe exponential form of the Fourier series () = () =9/4/20247测控技术与仪器英语教程2.3.1 Derivationthe exponential form of the Fourier series function9/4/20248测控技术与仪器英语教程2.3.2 Examples of Continuous Spectrathe spectrum of the isolated pulse waveform Figure 2.1 (a) A Signal isolated Pulse and (b)
5、 its Frequency Spectrum 9/4/20249测控技术与仪器英语教程2.3.2 Examples of Continuous SpectraThe spectrum of this pulse waveform illustrates a number of important points about time-limited signals. Figure 2.2 (a) Two isolated pulse, one of long and the other of short duration, and (b) their corresponding spectra
6、. Only a small part of the () spectrum of the short pulse is shown9/4/202410测控技术与仪器英语教程2.3.2 Examples of Continuous Spectraevaluate the spectrum of the exponentially decaying sinusoidal waveform =9/4/202411测控技术与仪器英语教程2.3.2 Examples of Continuous Spectraevaluate the spectrum of the exponentially deca
7、ying sinusoidal waveform9/4/202412测控技术与仪器英语教程2.3.3 Symmetry of the Fourier Integral EquationsThe description of Symmetry of the Fourier integral equations =9/4/202413测控技术与仪器英语教程2.3.3 Symmetry of the Fourier Integral EquationsThe description of Symmetry of the Fourier integral equations Figure2.4 Sym
8、metry between time and frequency domains. (a)just as a retangular pulse waveform has a (sinx/x) spectrum, so (b)a time function of (sinx/x)from has a rectangular spectrum, with energy equally distributed in the range 9/4/202414测控技术与仪器英语教程2.3.4 Limitations of the Fourier TransformLimitations of the F
9、ourier transformExample = =9/4/202415测控技术与仪器英语教程2.3.4 Limitations of the Fourier Transform9/4/202416测控技术与仪器英语教程2.3.4 Limitations of the Fourier TransformSingularityconvergence factor 9/4/202417测控技术与仪器英语教程2.4 The Laplace Transform2.4.1 Relationship with the Fourier Transform2.4.2 Use of the Laplace T
10、ransform2.4.3 The Pole-zero Description of a Signal9/4/202418测控技术与仪器英语教程2.4.1 Relationship with the Fourier TransformThe Laplace and Fourier transform are closely related 9/4/202419测控技术与仪器英语教程2.4.2 Use of the Laplace TransformExample) the decaying exponential waveform ) the sinusoidal wave 9/4/20242
11、0测控技术与仪器英语教程2.4.2 Use of the Laplace Transformthe decaying exponential waveform and the sinusoidal wave 9/4/202421测控技术与仪器英语教程2.4.2 Use of the Laplace Transformthe magnitude and phase of the decaying exponential wave (putting , ) Figure 2.7 Magnitude function and (b) phase function of the spectrum of
12、 the waveform of figure 2.6(a) 9/4/202422测控技术与仪器英语教程2.4.2 Use of the Laplace Transformthe inverse transform is defined asSolution: ) table of transform ) partial fractionsthe Laplace transform may be used to solve a great many problems other than those of signal analysis. 9/4/202423测控技术与仪器英语教程2.4.3
13、The Pole-zero Description of a SignalThe pole-zero description of a signal It is general property of such functions that there are values of the complex frequency variables which make G(s) tend to infinity and values of s which make G(s) zero; such values are known as the pole and zeros of G(s) resp
14、ectively 9/4/202424测控技术与仪器英语教程2.4.3 The Pole-zero Description of a Signalrepresent the poles and zeros of G(s) graphically by drawing their positions on a so-called Argand diagram , the real part of a complex variable is plotted along the abscissa, and the imaginary part along the ordinate. 9/4/2024
15、25测控技术与仪器英语教程Language in useVocabulary precious, appropriate, demonstrate, transform, decayStructureReading/writing techniques9/4/202426测控技术与仪器英语教程Vocabulary9/4/202427测控技术与仪器英语教程precious in dictionary昂贵的：价钱或价值很高的；值钱的珍贵的：受到高度评价的；珍藏的亲爱的；被热爱的矫揉造作的：矫饰地优美或过分文雅的十足的；纯粹的9/4/202428测控技术与仪器英语教程precious in text
16、In the previous chapter we have seen how a periodic signal may be expressed as the sum of a set of sinusoidal waves which are harmonically related.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。 9/4/202429测控技术与仪器英语教程precious in useprecious mannerisms.矫揉造作的习气a precious mess.一团糟9/4/202430测控技术与仪器英语教程appropriate in d
17、ictionary拨出：拨出作特殊用途挪用，窃用：为自己独自占有或使用，常未经许可9/4/202431测控技术与仪器英语教程appropriate in texteither as a set of sine and cosine waves of appropriate amplitude and frequency 或者表达为适当振幅和频率的一组正弦和余弦波 9/4/202432测控技术与仪器英语教程appropriate in useappropriating funds for education.拨款作教育基金Lee appropriated my unread newspaper
18、and never returned it.李擅自拿走我尚未阅读的报纸并从不归还9/4/202433测控技术与仪器英语教程visualize in dictionary形成思维图像；设想使可见9/4/202434测控技术与仪器英语教程visualize in textIt is indeed hard to visualize a wave such as an isolated pulse being composed of an infinite set of waves of infinitely small amplitudes .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
19、 .9/4/202435测控技术与仪器英语教程visualize in usetried to visualize the scene as it was described.尽力设想所描绘的场景9/4/202436测控技术与仪器英语教程demonstrate in dictionary表明：清楚细致地显示；表明证实，论证：通过推理或引证说明真实性；证明演示，说明：通过实验、例子或实际应用表明；解释并说明展示，示范：向可能的购买者示范（某物品的）使用9/4/202437测控技术与仪器英语教程demonstrate in textIt may seem strange that the puls
20、e contains no energy at such frequencies, but it is not hard to demonstrate. 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。 9/4/202438测控技术与仪器英语教程demonstrate in usedemonstrated her skill as a gymnast; demonstrate affection by hugging.显示她的体操技巧；拥抱以示亲热demonstrate a proposition.证明一个命题demonstrated the laws of physics with
21、 laboratory equipment.用实验装置演示物理定律The salesperson plugged in and demonstrated the vacuum cleaner.售货员插上电源，示范真空吸尘器的操作9/4/202439测控技术与仪器英语教程transform in dictionary使变形：明显地改变外观或形式改变的性质、职能或状况使变换使（一个结构）发生转换变压：使经过变压器的转换转变：使（一个细菌细胞）发生转化9/4/202440测控技术与仪器英语教程transform in textSo far it has been implied that the F
22、ourier transform may be successfully used for any no-repetitive signal, but there are in fact limitations and difficulties in its applications. 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。 9/4/202441测控技术与仪器英语教程transform in useA thick, fibrous fog had transformed the trees into ghosts and the stree
23、tlights into soft, haloed moons “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”9/4/202442测控技术与仪器英语教程decay in dictionary腐烂：分解成各组成部分；腐烂衰变：由于放射性衰变而解体或缩小衰减：指电压或电流的逐渐减弱能量衰减：指人造卫星在轨道上运行时能量消减衰亡，毁坏：使衰退：从正常、优秀或繁荣的状态衰败下去，恶化9/4/202443测控技术与仪器英语教程decay in textSuch terms give rise to not only the sine and cosine waves of the
24、Fourier method, but also growing and decaying sine and cosine waves and growing and decaying exponentials.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。9/4/202444测控技术与仪器英语教程decay in usea civilization that had begun to decay.已经开始衰落的文明9/4/202445测控技术与仪器英语教程Structure9/4/202446测控技术与仪器英语教程Reading / writing techniques9/4/202447测控技术与仪器英语教程
