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===Examples===
 
===Examples===
 
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==Autocorrelation and Autocovariance==
 
==Autocorrelation and Autocovariance==

Revision as of 19:55, 30 April 2013


Correlation vs Covariance

Student project for ECE302

by Blue



Correlation and Covariance

Correlation and covariance are very similarly related. Correlation is used to identify the relationship of two random variables, X and Y. In order to determine the dependence of the two events, the correlation coefficient,$ \rho $, is calculated as:

$ \rho (X,Y) = \frac{cov(X,Y)}{ \sqrt{var(X)var(Y)} } $

Covariance is defined as: $ C_{s}(n1, n2) = E(X-E[X])(Y-E[Y])) $[1] Correlation is then defined as: $ R_{s}(n1, n2) = E(XY) [2] $

If X and Y are independent of each other, that means they are uncorrelated with each other, or cov(X,Y) = 0. However, if X and Y are uncorrelated, that does not mean they are independent of each other. 1, -1, and 0 are the three extreme points $ p\rho X,Y) $ can represent. 1 represents that X and Y are linearly dependent of each other. In other words, Y-E[Y] is a positive multiple of X-E[X]. -1 represents that X and Y are inversely dependent of each other. In other words, Y-E[Y] is a negative multiple of X-E[X]. [1]

Examples

Correlation coefficient graph pxy0.png Correlation coefficient graph pxy0 2.png Correlation coefficient graph pxy4.png Correlation coefficient graph pxy-7.png Correlation coefficient graph pxy9.png Correlation coefficient graph pxy10.png Correlation coefficient graph pxy-10.png

Autocorrelation and Autocovariance

Correlation and covariance are comparing two random events. Autocorrelation and autocovariance are comparing the data points of one random event.

Autocovariance is defined as: $ C_{s}(n1, n2) = E(X_{n1}X_{n2}) [2] $

Autocorrelation is defined as: $ R_{s}(n1, n2) = E((X_{n1}-E[X_{n1}])(X_{n2}-E[X_{n2}])) [2] $


References

[1]: Ilya Pollak. General Random Variables. 2012. Retrieved from https://engineering.purdue.edu/~ipollak/ece302/SPRING12/notes/19_GeneralRVs-4_Multiple_RVs.pdf

[2]: Ilya Pollak. Random Signals. 2004. Retrieved from https://engineering.purdue.edu/~ipollak/ee438/FALL04/notes/Section2.1.pdf

Back to ECE302 Spring 2013, Prof. Boutin

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang