#RANDOM PROCESSES HOW TO#
#RANDOM PROCESSES PDF#

Likewise, mathematics can be viewed as an art form or a tool. We can hang the tool on our wall and step back and admire the fine craftmanship used to construct the hammer, or we can pick it up and use it to pound a nail into the wall. Mathematics is much like a well-crafted hammer. While the subject matter is primarily mathematical, it is presented for engineers. ※ See the example in pp.201~202 zero-mean Gaussian Random processĥ.This book is intended to be used as a text for either undergraduate level (junior/senior) courses in probability or introductory graduate level courses in random processes that are commonly found in Electrical Engineering curricula. 가정: statistically independent, that is, → mean of estimate = true mean If we measure X(t) at equally spaced time interval, that is, then the estimate of can be expressed as mean mean-square Estimation of the mean value of an ergodic random process → random variable 이며 true mean value 와 같지 않음 → 얼마나 에 가까운가? 의 mean이 와 같고 variance가 작아야 함!.Upon what aspects of measurement the goodness of the approximation depends?.

#RANDOM PROCESSES HOW TO#

How to estimate the process parameters from the observations of a single sample function? ← We cannot make an ensemble average for obtaining the parameters! if erogodic make a time average but, we cannot have a sample function over infinite time interval make a time average over a finite time interval  approximation to the true value → consider only one set of parameters if stationary X(t) at various times t these parameters are the same for all r.v. Statistical parameters of a random process = the sets of statistical parameters associated with the r.v.→ ergodic means stationary (not vice verse) ⇒ Ergodic processįor ergodic process, the mean values and moments can be determined by time averages as well as by ensemble averages, that is, (Note) This condition cannot exist unless the process is stationary. If Almost every member of the ensemble shows the same statistical behavior as the whole ensemble, then it is possible to determine the statistical behavior by examining only one typical sample function.are constant system analysis 결과는 strictly stationary 와 stationary in the wide sense의 두 경우 동일함! →구분하지 않고 사용 Random input response ⇒ stationary in the wide sense mean, mean-square, variance, correlation coefficient of any pair of r.v. mean value of any random variable X(t1) is independent of t1 & the correlation of two r.v. All maginal & joint density ftn should be independent of the time origin! ⇒ too stringent ⇒ relaxed condition

#RANDOM PROCESSES PDF#

Nonstationary random process: If any of the pdf does change with the choice of time origin, the process is nonstationary.

stationary random process: If all marginal and joint density function of the process do not depend on the choice of time origin, the process is said to be stationary (이 경우 모든 mean과 moment는 상수).

dependency of pdf on the value of time.

time t1 pdf 5.4 Stationary & Nonstationary Random Processes Remark : convenient way to obtain a probability model for signals that are known except for one or two parametersĮnsemble sample ftn X(t1) r.v. X(t1), X(t2), … and to determine pdf for r.v. (Example) X(t) = A cos(ωt + θ) A, ω … known constant θ … constant for all t but different for each sample function → random variation over the ensemble, not wrt time → still possible to define r.v.

deterministic random process : ~ can be exactly predicted ~.

nondeterministic random process : future values of each sample ftn cannot be exactly predicted from the observed past values (almost all random processes are nondeterministic).

mixed process : have both continuous and discrete componentĥ.3 Deterministic & Non deterministic Random Processes random ftn of time.

random variables can assume only certain isolated values.

PDF is continuous (pdf has NO δ function)ĭiscrete random process :.

random variables X(t1), X(t2), … can assume any value within a specified range of possible values.

Dependent on the possible values of the random variables.

more difficult is to relate the mathematical representations for random variables to the physical properties of the process ※ classification of random processes continuous / discrete deterministic / nondeterministic stationary / nonstationary ergodic / nonergodicĥ.2 Continuous & Discrete Random Processes.

How to extended the concepts of random variables to those of random processes? simple

Chapter 5 Random Processes ※ random process : a collection of time functions and an associated probability description marginal or joint pdf

Random processes