ECE4331_class2

# ECE4331_class2 - ECE 4371 Fall 2009 Introduction to...

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ECE 4371, Fall, 2009 Introduction to Telecommunication Introduction to Telecommunication Engineering Engineering Zhu Han Department of Electrical and Computer Engineering Class 2 Aug. 27 nd , 2009

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Outline Outline Chapter 2 and Some background suppose to be known, quick review, please read by yourself - Definition of Random Process - Stationary and Ergotic - Mean Correlation and Covariance - Power Spectral Density - Some Typical Random Process - Representation of Random Process
Deterministic and random processes Deterministic and random processes Deterministic processes: physical process is represented by explicit mathematical relation. Random processes: result of a large number of separate causes. Described in probabilistic terms and by properties which are averages. - The probability density function describes the general distribution of the magnitude of the random process, but it gives no information on the time or frequency content of the process time, t x(t) f X (x)

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Stationarity and Ergodicity Stationarity and Ergodicity Ensemble averaging : properties of the process are obtained by averaging over a collection or ‘ensemble’ of sample records using values at corresponding times Stationary random process : Ensemble averages do not vary with time. Example 1.1 Time averaging : properties are obtained by averaging over a single record in time Ergodic process : Stationary process in which averages from a single record are the same as those obtained from averaging over the ensemble. In other word, average over different random process with the same distribution is equal to the average of one random process over time.
Mean Mean The mean value, f8e5 x , is the height of the rectangular area having the same area as that under the function x(t) Can also be defined as the first moment of the p.d.f.

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ECE4331_class2 - ECE 4371 Fall 2009 Introduction to...

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