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Unformatted text preview: 1 Random (Stochastic) Process Random signals (voice, T.V., Digital computer data, electrical noise) have two properties: Function of time (defined in some interval) Random (impossible to describe exactly the waveforms) An indexed set of functions of some parameter ( t,d..) that has some statistical properties 2 Note that to qualify as a R.P., x could be a function of any other variable (distance for example) and a function of more than one variable. Outcome of the First trial of The experiment Outcome of the 2 nd trial of The experiment ( sample function ) Outcome of the n th trial of The experiment x 1 (t ) x 2 (t ) x n (t ) x 1 (t k ) x 2 (t k ) x n (t k ) s 1 s 2 s n Sample space S ( ensemble ) 3 Example: Consider the voltage waveforms emitted from a noise source One possible waveform is x(t,E i ) is a sample function of the sample space All possible sample functions is called the ensemble and defines the random process x(t) that describes the noise source A random process maps events into functions of the parameter t . (R.V. maps events into constants) 4 But the noise voltage is function of time. Thus the R.V. x is a function of time and can be expressed as x (t) A R.V that is a function of time is called a random process (or stochastic process) To continue with the example of the random process x(t), we need to record noise voltage for each t in order to specify the random process. We obtain many waveforms, ( called sample function ). Sample function amplitudes at some instant t=t 1 are x(t 1 ) in various trials The collection of all possible waveforms is called ensemble (sample space) of the random process 5 How to specify a random process ?...
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This note was uploaded on 03/19/2012 for the course ELCN 306 taught by Professor Hebatmourad during the Spring '10 term at Cairo University.
 Spring '10
 HebatMourad

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