Wide sense stationary
In mathematics, a stationary process (or strict(ly) stationary process or strong(ly) stationary process) is a stochastic process whose joint probability distribution does not change when shifted in time or space. Consequently, parameters such as the mean and variance, if they are present, also do not change over time or position. As a result, the mean and the variance of the process do not follow trends.
Stationarity is used as a tool in time series analysis, where the raw data are often transformed to become stationary; for example, economic data are often seasonal and/or dependent on a non-stationary price level. An important type of non-stationary process that does not include a trend-like behavior is the cyclostationary process.
Note that a "stationary process" is not the same thing as a "process with a stationary distribution".[clarification needed] Indeed there are further possibilities for confusion with the use of "stationary" in the context of stochastic processes; for example a "time-homogeneous" Markov chain is sometimes said to have "stationary transition probabilities". Besides, all stationary Markov random processes are time-homogeneous.

This is an excerpt from the article Wide sense stationary from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article Wide sense stationary at en.wikipedia.org was accessed 233 times in the last 30 days. (as of: 11/13/2013)
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Stationary process - Wikipedia, the free encyclopedia
Any strictly stationary process which has a mean ... The main advantage of wide-sense stationarity is ...
en.wikipedia.org/wiki/Stationary_process
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Wide-Sense Stationary Example Example (continued)
Linear Filtering of Random Processes. Lecture 13. Spring 2002. Wide-Sense Stationary. A stochastic process X(t) is wss if its mean is constant. E[X(t)] = µ.
www.cis.rit.edu/class/simg713/Lectures/Lecture713-13-4.pdf
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Wide Sense Stationary Random Processes - Springer
Having introduced the concept of a random process in the previous chapter, we now wish to explore an important subclass of stationary random processes.
link.springer.com/chapter/10.1007%2F0-387-24158-2_17
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• Strict and Wide Sense Stationarity • Autocorrelation Function of a ...
Strict and Wide Sense Stationarity. • Autocorrelation Function of a Stationary Process. • Power Spectral Density. • Response of LTI System to WSS Process Input.
opencourses.emu.edu.tr/mod/resource/view.php?id=170&redirect=1
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Stationary and wide sense stationary (WSS) processes
Stationary and Wide sense stationary Processes. Guy Lebanon. January 6, 2006 . Definition 1. A RP X = {Xt : t ∈ R} or X = {Xn : n = ..., −2, −1, 0, 1, 2,.
www.cc.gatech.edu/~lebanon/notes/stationarity.pdf
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8 - Wide-sense stationary processes - University Publishing Online
The remaining chapters of the book deal with complex-valued random processes . In this chapter, we discuss wide-sense stationary (WSS) signals. In Chapter 9 ...
ebooks.cambridge.org/chapter.jsf?bid=CBO9780511815911&cid=CBO9780511815911A068
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Handout #11: Lecture notes on Random Processes - Venugopal V ...
18 Mar 2003 ... Wide Sense Stationarity: A random process X(t) is said to be wide sense ... If a process is strictly stationary, it is also WSS – of course, the ...
vvv.ece.illinois.edu/ece359/handouts/h11.pdf
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Signals, Systems and Inference, Chapter 9: Random Processes
(ti − tj ), then the process is said to be wide-sense stationary (WSS). Clearly a process that is SSS is also WSS. For a WSS random process X(t), therefore, we.
ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-011-introduction-to-communication-control-and-signal-processing-spring-2010/readings/MIT6_011S10_chap09.pdf
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Stationary process - Wikipedia, the free encyclopedia
In mathematics and statistics, a stationary process (or strict(ly) stationary process or strong(ly) stationary process) is a stochastic process whose joint ...
en.wikipedia.org/wiki/Wide-sense_stationary
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wide-ranging - definition of wide-ranging by The Free ...
wide-rang·ing (wīd′rān′jĭng) adj. Covering a wide area; including much: a pianist's wide-ranging repertoire; a wide-ranging interview. Thesaurus ...
www.thefreedictionary.com/wide-ranging
Search results for "Wide sense stationary"
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Wide sense stationary in science
8 - Wide-sense stationary processes - University Publishing Online
The remaining chapters of the book deal with complex-valued random processes . In this chapter, we discuss wide-sense stationary (WSS) signals. In Chapter 9 ...
Wide Sense Stationary Random Processes - Springer
Such a random process is said to be stationary in the wide sense or wide sense ... Dept. of Electrical & Computer Engineering, University of Rhode Island, ...
Stationary process - Wikipedia, the free encyclopedia
Any strictly stationary process which has a mean ... The main advantage of wide-sense stationarity is ...
[PDF]An Ergodic Theorem for the Square of a Wide-sense Stationary ...
BY A. LARRY WRIGHT. University of Arizona. Let {X(t), -co < t < oo} be a stochastic process which is stationary in the wide sense with spectral representation.
The Wiener-Khinchin Theorem for Non-wide Sense stationary ...
Publication » The Wiener-Khinchin Theorem for Non-Wide sense stationary Random Processes. ... Wei Lu. Iowa State University ...
Generation of Non-Gaussian Wide-Sense Stationary Random ...
Generation of Non-Gaussian Wide-Sense Stationary Random Processes with ... of Finite Element Analysis and CAD, Peking University Press, Beijing, 1994, pp.
[PDF]• Strict and Wide Sense Stationarity • Autocorrelation Function of a ...
Strict and Wide Sense Stationarity. • Autocorrelation Function of a Stationary Process. • Power Spectral Density. • Response of LTI System to WSS Process Input.
The Wiener-Khinchin Theorem for Non-wide Sense stationary ...
Apr 3, 2009 ... Abstract: We extend the Wiener-Khinchin theorem to non-Wide sense stationary ( WSS) random processes, i.e. we prove that, under certain ...
condition for a ARMA process to be wide-sense stationary
Apr 30, 2014 ... some (e.g. in Tsay's Financial Time Series) said: it is wide-sense stationary, iff all the roots of its AR characteristic polynomial are greater than 1 ...
[PDF]SC505 STOCHASTIC PROCESSES Class Notes - MIT
Boston University .... 3.9 Power Spectral Density of Wide-Sense Stationary Processes . ... 5.5 Second-order Statistics for Vector-Valued Wide-Sense Stationary ...
Books on the term Wide sense stationary
Biomedical Signal and Image Processing, Second Edition
Kayvan Najarian, Robert Splinter, 2012
6.4.2 StAtionAry AnD ergoDic StocHAStic proceSSeS A.subset.of.stochastic. processes.provides.some.practically.useful.characteristics..This. family.that.is. referred.to.as.“stationary.processes.in.wide.sense”.in.which.the.mean.
Fundamentals of Applied Probability and Random Processes
Oliver Ibe, 2014
Find the autocorrelation function RXX (t,t+τ), and show that X(t) is a wide-sense stationary process b. Find the autocorrelation function RYY (t,t+τ), and show that Y(t) is a wide-sense stationary process c. Find the crosscorrelation function RXY ( t ...
Stochastic Processes and Their Applications
Frank Beichelt, L. Paul Fatti, 2001
Definition 2.3 (wide-sense stationarity) A second order process is said to be wide -sense stationary (stationary in wide sense) if it has properties (2.11) and (2.13). • A strictly stationary process is not necessarily a wide-sense stationary process, ...
Stochastic Processes: Theory for Applications
Stochastic Processes: Theory for Applications
Robert G. Gallager, 2014
This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review ...
Advanced Digital Signal Processing and Noise Reduction
Saeed V. Vaseghi, 2008
In signal processing theory, two classes of stationary processes are defined: (a) strict-sense stationary processes and (b) wide-sense stationary processes, which is a less strict form of stationarity, in that it only requires that the first-order and ...
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Wide sense stationary
Stationary process - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Stationary_process
Cyclostationary process - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Cyclostationary_process
Spectral factorization of wide sense stationary processes on Z2
www.sciencedirect.com/science/article/pii/0047259X86900928
probability theory - Is wide sense stationary iff second order stationary? - Mathematics Stack Exchange
math.stackexchange.com/questions/645226/is-wide-sense-stationary-iff-second-order-stationary
stochastic calculus - About stationary and wide-sense stationary processes - Mathematics Stack Exchange
math.stackexchange.com/questions/540055/about-stationary-and-wide-sense-stationary-processes
Wide-sense stationary - What does WSS stand for?
What does WSS stand for? Definition of Wide-sense stationary in the list of acronyms and abbreviations provided by the Free Online Dictionary and Thesaurus.
acronyms.thefreedictionary.com/Wide-sense+stationary
Generation of Non-Gaussian Wide-Sense Stationary Random Processes with Desired PSDs and PDFs
This paper describes a new method to generate discrete signals with arbitrary power spectral density (PSD) and first order probability density function (PDF) without any limitation on PDFs and PSDs. The first approximation has been achieved by using a nonlinear transform function. At the second stage the desired PDF was approximated by a number of symmetric PDFs with defined variance. Each one provides a part of energy from total signal with different ratios of remained desired PSD. These symmetric PDFs defined by sinusoidal components with random amplitude, frequency and phase variables. Both analytic results and examples are included. The proposed scheme has been proved to be useful in simulations involving non-Gaussian processes with specific PSDs and PDFs.
www.scirp.org/journal/PaperInformation.aspx?PaperID=24957
WSS - Wide-Sense Stationary
What does WSS stand for? WSS stands for Wide-Sense Stationary. This definition appears very rarely The World's most comprehensive professionally edited abbreviations and acronyms database
www.acronymfinder.com/Wide_Sense-Stationary-(WSS).html
WSS-US - Wide-Sense Stationary - Uncorrelated Scattering
What does WSS-US stand for? WSS-US stands for Wide-Sense Stationary - Uncorrelated Scattering. This definition appears very rarely The World's most comprehensive professionally edited abbreviations and acronyms database
www.acronymfinder.com/Wide_Sense-Stationary-_-Uncorrelated-Scattering-(WSS_US).html
The Wiener-Khinchin Theorem for Non-wide Sense stationary Random Processes - CERN Document Server
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