1、Lesson 4 Random Signals Backgrounds Text tour Language in use Vocabulary Structure Reading/writing techniques2022-8-41测控技术与仪器英语教程Backgrounds Terminology Bayesrule 贝叶斯公式 Correlation function 相关函数 Morse code 莫尔斯码 Neurophysiology 神经生理学 Normal distribution 正态分布 Poisson distribution 泊松分布 Probability 概率 S
2、tandard deviation 标准偏差 Time-shifted version 时移形式 Expect 期望 Standard deviation 标准方差2022-8-42测控技术与仪器英语教程Text tour Outline 4.1 Introduction4.2 Elements of Probability Theory4.3 Amplitude Distribution and Moments4.4 The Autocorrelation and Power Spectral Density 2022-8-43测控技术与仪器英语教程4.1 Introduction The
3、background of random signals Example about several signalsFigure 4.1 Signal displaying(a)random amplitude,(b)random timing of transition between fixed levels,and(c)random amplitude and timing components in an essentially repetitive waveform.2022-8-44测控技术与仪器英语教程4.1 Introduction The origin of random s
4、ignal and the way of dealing with it 2022-8-45测控技术与仪器英语教程4.2 Elements of Probability Theory4.2.1 The probability of an Event4.2.2 Joint and Conditional Probabilities4.2.3 The Probability Density Function2022-8-46测控技术与仪器英语教程4.2.1 The Probability of an Event Using examples to define the probability of
5、 an event the basic additive law of probability =)(lim)(NnApN)(lim)(lim)(lim)(NmNnNmnAorBpNNN)()(BpAp2022-8-47测控技术与仪器英语教程4.2.2 Joint and Conditional Probabilities The joint probability The conditional probabilities The Bayes rule,relates the conditional probability of A given B to that of B given A.
6、)(lim)(lim)(nmNnNmAandBpNN)/()()(ABpApAandBp)()()(BApApAandBp)()()()(BApBpABpAp)()()()(BpABpApBAp2022-8-48测控技术与仪器英语教程4.2.2 Joint and conditional probabilities The statistically independent The joint and conditional probabilities relevance to signals and signal analysis Figure 4.2(a)A portion of a ra
7、ndom sampled-data signal with six discrete levels and(b)the probabilities associated with each level)()(ABpAp)()()(BpApAandBp2022-8-49测控技术与仪器英语教程4.2.3 The Probability Density Function the probability density function Figure 4.3 A continuous random signalyyporqyqyp)()(2022-8-410测控技术与仪器英语教程4.2.3 The P
8、robability Density Function Example1111)(2)1(1yypyy5.0)(1yp-11y=00.5y1y1y)(yFigure 4.4 A rectangular probability density function2022-8-411测控技术与仪器英语教程 4.3 Amplitude Distribution and Moments amplitude distributions:)deterministic signals A-At=0t(a)A1-AAy)(y(b)Figure 4.5(a)Part of a continuous sinusoi
9、dal wave of amplitude A,and(b)its amplitude probability density2022-8-412测控技术与仪器英语教程4.3 Amplitude Distribution and Moments )the amplitude distribution of a signal tells us nothing about its detailed structure or spectrum,nor is it a unique property of the signal.Figure 4.6 Portions of four waveforms
10、 with identical amplitude distributions adyypaP)()(2022-8-413测控技术与仪器英语教程4.3 Amplitude Distribution and Moments The first central moment is also called the expected The second central moment is referred to as the standard deviation.nmmmypy1dyypyy)(nmmmpyyyy1222)()(dyypyyyym)()()(2222022-8-414测控技术与仪器英
11、语教程4.3 Amplitude Distribution and Moments the central moments and moments are closely related 222)(yy2022-8-415测控技术与仪器英语教程4.4 The Autocorrelation and Power Spectral Density4.4.1 The Spectral Properties of Random Signals4.4.2 The Autocorrelation Function4.4.3 The Power Spectral Density Function2022-8
12、-416测控技术与仪器英语教程4.4.1 The Spectral Properties of Random Signals The spectral measure of random signals is very useful Figure 4.72022-8-417测控技术与仪器英语教程4.4.2 The Autocorrelation Function The autocorrelation function(ACF)of a signal waveform is an average measure of its time-domain properties finite ACF
13、220000)()(1lim)(TTTxxdttftfTrdttftfrxx)()()(112022-8-418测控技术与仪器英语教程4.4.2 The Autocorrelation Function the shift is equal to a multiple of the sampling interval T some of ACFs principal properties NNmkmmTxxxxNkr)12(1lim)(0)cos()cos()(222111tAtAtf22212111cos2cos2)(AAr2022-8-419测控技术与仪器英语教程4.4.2 The Aut
14、ocorrelation FunctionFigure 4.8 (a)A signal with two discrete frequency components,and(b)its autocorrelation function2022-8-420测控技术与仪器英语教程4.4.2 The Autocorrelation Function The peak value of ACF is given by 22200000)(1lim)0()(TTTxxxxdttfTrrdttfrxx2)()0(2022-8-421测控技术与仪器英语教程4.4.3 The Power Spectral D
15、ensity Function power spectrum,power spectral,density energy spectrum Figure 4.9(a)A signal and its autocorrelation function,and(b)their corresponding frequency-domain descriptions and involves both magnitude and phase terms,whereas is purely real2022-8-422测控技术与仪器英语教程4.4.3 The Power Spectral Density
16、 Function The relation between the ACF and power spectrum,or power spectral density derPjxxxx)()(dePrjxxxx)(21)(2022-8-423测控技术与仪器英语教程Language in use Vocabulary calculate,transmit,random,convey,obvious,identical Structure Reading/writing techniques2022-8-424测控技术与仪器英语教程Vocabulary2022-8-425测控技术与仪器英语教程c
17、alculate in dictionary 计算：通过计算来确认；计算 估计：做出估计；估价 考虑，设想：为特定目的安排；设计 推测：计划、打算或计数2022-8-426测控技术与仪器英语教程calculate in text Such signals are described as deterministic,and the frequency spectra we calculate for them specify the magnitudes and relative phases of the sinusoidal wave which,if add together,would
18、 exactly resynthesise the original waveforms.这类信号被描述成“确定性”信号，由它们所得出的频谱详细表述了正弦波的幅值和相对相位，如果将这些正弦波叠加起来就会很精确的合成为原波形。2022-8-427测控技术与仪器英语教程calculate in use calculating the area of a circle;calculated their probable time of arrival.计算圆的面积；计算他们可能的抵达时间 calculating the teams chances of winning.估计该队获胜的可能 a stu
19、rdy car that is calculated to last for years;a choice that was calculated to please.设计能耐用多年的牢固汽车；一项为取悦而设计的选择 I callate shes a right smart cook 我猜测她是一位手艺精巧的厨师2022-8-428测控技术与仪器英语教程transmit in dictionary 传送：从一个人、事物或地点传送到另一人、事物或地点；传染：使传播；传染 遗传：通过遗留或继承的方式给予或传达给另一个人；传下去 传播：传播（消息或信息）；交流 传送：通过电线或无线电等传送（信号）传
20、导：在通过一个媒质时产生的（振动）传到：把（力或能量）从机械装置的一个部分传到另一个部分2022-8-429测控技术与仪器英语教程transmit in text As a simple example,it would be pointless to transmit a continuous sinusoidal tone,sine once its amplitude,frequency and phase characteristics have been determined by the receiver,no further information is conveyed.一个简
21、单的例子是，传送一个连续的正弦音是无意义的，因为一旦接收者确定了正弦的振幅、频率和相位特性，就没有进一步的信息传送了。2022-8-430测控技术与仪器英语教程transmit in use transmit an infection.传播传染渍2022-8-431测控技术与仪器英语教程random in dictionary 没有具体形式、目的或内容的：随机的：同组中每个成员都有相同或平等机会或可能出现的2022-8-432测控技术与仪器英语教程random in text A signal may be random in a variety of ways,perhaps the mos
22、t common type of randomness is in the amplitude of a signal waveform,illustrated in figure 4.1(a).信号的随机性表现在各方面，或许最普遍的随机性是在信号的振幅上，如图4.1(a)所示。2022-8-433测控技术与仪器英语教程random in use random movements;a random choice.随意运动；一个随意的选择2022-8-434测控技术与仪器英语教程convey in dictionary 传送：将从一个地方运送或输送到另一个地方；输送 传播：作为的传送或传播媒介；
23、传播 交流或使知道；告知 将财产权或头衔转让给2022-8-435测控技术与仪器英语教程convey in text no further information is conveyed.没有进一步的信息传送了。2022-8-436测控技术与仪器英语教程convey in use wires that convey electricity.传电的金属线 a look intended to convey sympathetic comprehension 脸上的神情想要传达同情与谅解2022-8-437测控技术与仪器英语教程obvious in dictionary 明显的：容易感到或理解的；
24、易看透的：因为不精巧而容易被看穿；透明的：挡路的：站在路中或前面的2022-8-438测控技术与仪器英语教程obvious in text It is obvious that if outcome B is completely unaffected by outcome A 显然，如果结果和结果相互完全不影响 2022-8-439测控技术与仪器英语教程obvious in use an obvious political ploy.一个易被识破的政治手法2022-8-440测控技术与仪器英语教程identical in dictionary 同一的：完全相等的或相似的 可互换的：十分类似或
25、相象以至于本质上相等的或能互换的 同卵双生的：从同一受精卵中产生的，具有相同基因结构和相似外貌的孪生子的；单卵的2022-8-441测控技术与仪器英语教程identical in text These equations are identical in form to the Fourier transform pair which relate a signal f(t)to its spectrum ,expect that we are now working in terms of the delay variable rather than the time variable t.我们使用的是延时变量而不是时间变量的话，通过傅立叶变化和反变换可以把信号f(t)和它的频谱相对应起来，按照傅立叶变换和反变换的形式，这些等式是完全相同的。)(jG2022-8-442测控技术与仪器英语教程identical in use another orator who used the senators identical words.另一个发言者使用了与这个参议员完全相同的措词2022-8-443测控技术与仪器英语教程Structure2022-8-444测控技术与仪器英语教程Reading/writing techniques2022-8-445测控技术与仪器英语教程
