[信息与通信]测控技术与仪器英语教程 Lesson 2 Aperiodic Signal

1、lesson 2 aperiodic signal backgrounds text tour language in use vocabulary structure reading/writing techniques2021-10-151测控技术与仪器英语教程backgrounds terminology 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

2、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 2021-10-152测控技术与仪器英语教程text tour outline2.1 introduction2.2 the exponential form of the fourier series2.3 the fourier transform2.4 the laplace transform2021-10-153测控技术与仪器英语教程2.1 introduction the introduction of aperiodic signal2021-

3、10-154测控技术与仪器英语教程2.2 the exponential form of the fourier seriesthe exponential form of the fourier series =analysis)exp()2exp(1112tjatjaf)2exp()exp(1110tjatjaammtjma)exp(12021-10-155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

4、integral equations2.3.4 limitations of the fourier transform2021-10-156测控技术与仪器英语教程2.3.1 derivation the exponential form of the fourier series () = () =mmtjmatf)exp()(1dxjmxxfam)exp()(21dttjmtf)exp()(1dtetfgtj)()()exp()()(1tjmtgtf)exp(2)(11tjmgdegtftj)(21)(2021-10-157测控技术与仪器英语教程2.3.1 derivation the e

5、xponential form of the fourier series function2021-10-158测控技术与仪器英语教程2.3.2 examples of continuous spectra the spectrum of the isolated pulse waveform figure 2.1 (a) a signal isolated pulse and (b) its frequency spectrum )sin(211)(tjtjejdteg2021-10-159测控技术与仪器英语教程2.3.2 examples of continuous spectra th

6、e 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. only a small part of the () spectrum of the short pulse is shown2021-10-1510测控技术

7、与仪器英语教程2.3.2 examples of continuous spectra evaluate the spectrum of the exponentially decaying sinusoidal waveform =dtetfgtj)()(00sindtetetjat)exp()exp(21sin000tjtjjt2)(22020jg2021-10-1511测控技术与仪器英语教程2.3.2 examples of continuous spectra evaluate the spectrum of the exponentially decaying sinusoidal

8、waveformt=0tatefigure2.32021-10-1512测控技术与仪器英语教程2.3.3 symmetry of the fourier integral equations the description of symmetry of the fourier integral equations =dtetfgtj)()(degtftj)(21)()()()(t detfgtjt detftj)(t detfgtj)()(2021-10-1513测控技术与仪器英语教程2.3.3 symmetry of the fourier integral equations the de

9、scription of symmetry of the fourier integral equations figure2.4 symmetry 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 2021-10-1514测控

10、技术与仪器英语教程2.3.4 limitations of the fourier transform limitations of the fourier transform example = =dtetfgtj)()(dttf)(0)(dteegtjt0)(1tteej) 10()(1)(jg0,)(1forj2021-10-1515测控技术与仪器英语教程2.3.4 limitations of the fourier transformt=0lttet=0t(a)(b)figure2.5 (a)the unit step function, and (b) an expotential

11、ly decaying stepfunction2021-10-1516测控技术与仪器英语教程2.3.4 limitations of the fourier transform singularity convergence factor 0)01)()(dtetfdteegtjtjtdtetfgst01)()(2021-10-1517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 transform2.4.3 the pole-

12、zero description of a signal2021-10-1518测控技术与仪器英语教程2.4.1 relationship with the fourier transform the laplace and fourier transform are closely related 2021-10-1519测控技术与仪器英语教程2.4.2 use of the laplace transform example) the decaying exponential waveform ) the sinusoidal wave )(11)()(0)()(0sesdtedtetfs

13、gtssst)()exp(sin)(00000jsjsdtstsg2021-10-1520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 t=0ttet=0tt0sin0/(a)(b)figure 2.62021-10-1521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 (putt

14、ing , ) figure 2.7 magnitude function and (b) phase function of the spectrum of the waveform of figure 2.6(a) )(1)(jgjs 2021-10-1522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 s

15、olve a great many problems other than those of signal analysis. jjstdsesgjtf)(21)(2021-10-1523测控技术与仪器英语教程2.4.3 the pole-zero description of a signal the 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)

16、 tend to infinity and values of s which make g(s) zero; such values are known as the pole and zeros of g(s) respectively )(1)(ssg2021-10-1524测控技术与仪器英语教程2.4.3 the pole-zero description of a signal represent the poles and zeros of g(s) graphically by drawing their positions on a so-called argand diagr

17、am , the real part of a complex variable is plotted along the abscissa, and the imaginary part along the ordinate. 2021-10-1525测控技术与仪器英语教程language in use vocabulary precious, appropriate, demonstrate, transform, decay structure reading/writing techniques2021-10-1526测控技术与仪器英语教程vocabulary2021-10-1527测

18、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2021-10-1528测控技术与仪器英语教程precious in text 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

19、周期信号是如何被表示成一组正弦谐波的叠加。 2021-10-1529测控技术与仪器英语教程precious in use precious mannerisms. 矫揉造作的习气 a precious mess. 一团糟2021-10-1530测控技术与仪器英语教程appropriate in dictionary 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2021-10-1531测控技术与仪器英语教程appropriate in text either as a set of sine and cosine waves of appropriate amplitude

20、 and frequency 或者表达为适当振幅和频率的一组正弦和余弦波 2021-10-1532测控技术与仪器英语教程appropriate in use appropriating funds for education. 拨款作教育基金 lee appropriated my unread newspaper and never returned it. 李擅自拿走我尚未阅读的报纸并从不归还2021-10-1533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2021-10-1534测控技术与仪器英语教程visualize in text

21、 it 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 .2021-10-1535测控技术与仪器英语教程visualize in use tried to visualize the scene as it was described. 尽力设想所描绘的场景2021-10-1536测控技术与仪器英语教程demonst

22、rate 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2021-10-1537测控技术与仪器英语教程demonstrate in text it may seem strange that the pulse 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。 2021-10-1538

23、测控技术与仪器英语教程demonstrate in use demonstrated 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 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

24、尘器的操作2021-10-1539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2021-10-1540测控技术与仪器英语教程transform in text 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. 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