# Lect8 - Stochastic Process Lecture 8 Random Sequence(1...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Stochastic Process 11/17/2006 Lecture 8 Random Sequence (1) NCTUEE Summary In this lecture, I will discuss: • Random Sequence • Stationarity • Wide-sense Stationary Random Sequence Notation We will use the following notation rules, unless otherwise noted, to represent symbols during this course. • Boldface upper case letter to represent MATRIX • Boldface lower case letter to represent vector • Superscript ( · ) T and ( · ) H to denote transpose and hermitian (conjugate transpose), respectively • Upper case italic letter to represent RANDOM VARIABLE 8-1 1 Random Sequence (1) In plain words, we can view a random sequence as follows: → A mathematical model of a probabilistic experiment that evolves in time → A random sequence can be considered as an evolution in time of random variables * The outcomes constitute a sequence of numerical values * The outcomes are measured in countable time instants, e.g. the time instants in the set T = { , 1 , 2 , ···} or T = {··· ,- 1 , , 1 , 2 , ···} . (2) For example, a random sequence can be used to model → the sequence of daily prices of a stock → the sequence of hourly traffic loads at a node of a network → the sequence of radar measurement of the position of an airplane → the sequence of failure times of a machine → the sequence of received and periodically sampled signal in a com- munication link (3) Something of particular interests: → We tend to focus on the dependencies in the sequence. For example, how do future prices of a stock depend on past values? → We are often interested in long-term averages , involving the entire sequence of generated values. For example, what is the fraction of time that a machine is idle? → We sometimes wish to characterize the likelihood or frequency of certain boundary events. For example, what is the probability that within a given hour all circuits of some telephone system become simultaneously busy, or what is the frequency with which some buffer in a computer network overflows with data? 8-2 ] [ X n ] 1 [ X + n ] 1 [ X- n n θ 1- n θ 1 + n θ (i) (ii) (iii) Figure 1 : The (i) filtering, (ii) smoothing, and (iii) prediction operations for time-varying unknown parameters θ n embedded in the random sequence X [ n ] for all n ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 13

Lect8 - Stochastic Process Lecture 8 Random Sequence(1...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online