《测量与信号基础英文PPT (21).pdf》由会员分享，可在线阅读，更多相关《测量与信号基础英文PPT (21).pdf（21页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、Contents Chapter 1 Introduction Chapter 2 Time Waveform Analysis Chapter 3 Frequency Spectrum Analysis Chapter 4 Amplitude Possibility Analysis Chapter 5 Time delay Correlation Analysis Chapter 6 Time-varying signal analysis Chapter 7 Signal Filtering Chapter 8 Principles of sensors Chapter 9 Signal
2、 conditioning technique Chapter 10 Characteristics of measurement systems Chapter 11 Computer based measurement systems Signal analysis Measurement Fundamentals of Measurement and Signal Analysis Chapter 5 Time delay Correlation Analysis Fundamentals of Measurement and Signal Analysis 5.1 Concepts o
3、f correlation analysis 1)Variable correlation(correlation coefficient)In statistics,the correlation coefficient is used to describe the correlation between the variable x and y.It is the mathematical expectation of the product of two random variables,which characterizes the degree of correlation bet
4、ween x and y.cxuyxyxyxyixiyixiy()()()*()xy222A change in the value of one variable can predict the change in the value of another variable.ux=mean(x);uy=mean(y);xa=x-ux;ya=y-uy;p=sum(xa.*ya)/sqrt(sum(xa.*xa)*sum(ya.*ya);Matlab Codes 5.1 Concepts of correlation analysis xy0.82xy1xy-0.95xy-1xy0.015xy0
5、.005Positive correlation Perfect positive relationship Negative correlation No correlation Perfect negative relationship No correlation xxxxyyyyyyIn a positive correlation,the amount of one variable increases,the amount of another variable also increases.In a negative correlation,the amount of one v
6、ariable increases,the amount of another variable decrease.5.1 Concepts of correlation analysis Example:Temperature and Humidity Data of Wuhan in 2020/05/22 H=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23;Tem=20 19 18 18 17 17 17 20 22 24 26 27 28 28 29 30 30 31 29 24 22 21 21 20;Hum=
7、93 95 96 97 98 98 99 100 85 74 63 61 57 57 53 50 50 44 50 71 77 85 87 92;subplot(3,1,1);plot(H,Tem,-,H,Tem,*);grid on;xlim(0,24);ylim(15,35);subplot(3,1,2);plot(H,Hum,-,H,Hum,*);grid on;xlim(0,24);ylim(40,100);subplot(3,1,3);plot(Tem,Hum,*);grid on;xlim(15,35);ylim(40,100);x=Tem;y=Hum;ux=mean(x);uy=
8、mean(y);xa=x-ux;ya=y-uy;p=sum(xa.*ya)/sqrt(sum(xa.*xa)*sum(ya.*ya)xy-0.9872Temperature Temperature Humidity Humidity Hour Hour xuyxyixiyixiy()()()*()xy2225.1 Concepts of correlation analysis 2)Signal correlation(correlation function)2122/)()()()()(dttydttxdttytxxyIf the variable x and y are time-rel
9、ated functions,i.e.,x(t)and y(t),then the correlation coefficient of two variables is a function of time dependent,it is called the correlation function of signals.xuyxyixiyixiy()()()*()xy222It is the correlation between two waveforms at the time delay point.5.1 Concepts of correlation analysis ty()
10、tx t()ttdy(-T)tTdtdy(T)t-Td 0.055.1 Concepts of correlation analysis Example of a sine signal and a cosine signal y tt()5*cos(2 5);x tt()2*sin(2 5);00.000240.051xuyxyixiyixiy()()()*()xy2225.1 Concepts of correlation analysis y t()x t()()x()y()5.1 Concepts of correlation analysis In engineering,peopl
11、e usually care about the shape of the correlation function,instead of their specific values,so the formula can be simplified.2122/)()()()()(dttydttxdttytxxy()()()xyRx t y tdtX The cross-correlation Function The auto-correlation function()()()xRx t x tdt5.1 Concepts of correlation analysis 3)Cross-co
12、rrelation function The cross-correlation function is a measure of similarity between two signals.()()()xyRx t y tdtExample：The Clap signal recorded by two MICs in a distance interval of 2M 5.1 Concepts of correlation analysis MIC 2 Sound MIC 2M Speed of electromagnetic waves in the wire：3 108 m/s Td
13、？Speed of sound in air：340m/s（25）VD/Td()()()xyRx t y tdt0.006s V2/0.0063335.1 Concepts of correlation analysis Calculation process x t()xyR()ty()()()()xyRx t y tdt5.1 Concepts of correlation analysis Calculation process()()()xyRx t y tdtAnalysis of the clap signal by Adobe Audition 2=0 point 5.1 Con
14、cepts of correlation analysis 5.1 Concepts of correlation analysis 4)Autocorrelation function Speed of sound in air：340m/s（25）Echo Example：Time delay of Echo Td？VdD*T/2The auto-correlation function is a measure of similarity between a signal and its time delayed version.5.1 Concepts of correlation a
15、nalysis()()()xRx t x tdtTd2.062s 5.1 Concepts of correlation analysis Calculation process()()x()xRx ttdt 5.1 Concepts of correlation analysis Calculation process()()x()xRx ttdtHomeworks 5.1 Concepts of correlation analysis 1.What is the purpose of correlation analysis?2.What is the difference between auto-correlation analysis and cross-correlation analysis?Fundamentals of Measurement and Signal Analysis