Wide-sense stationary process
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 process from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
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Stationary process - Wikipedia, the free encyclopedia
[edit]. A weaker form of stationarity commonly employed in signal processing is known as weak-sense ...
en.wikipedia.org/wiki/Stationary_process
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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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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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Wide-Sense Stationary Example Example (continued)
Lecture 13. Spring 2002. Wide-Sense Stationary. A stochastic process X(t) is wss if its mean is constant. E[X(t)] = µ and its autocorrelation depends only on τ = t1 ...
www.cis.rit.edu/class/simg713/Lectures/Lecture713-13-4.pdf
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Stationary and Wide Sense Stationary 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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Lecture 3: Stationary Processes
1.4 Continuous time processes stationary in wide sense. 1.5 Prediction and interpolation problems. 2. Stationary processes. 2.1 Stationary processes in strong ...
kurser.math.su.se/mod/resource/view.php?id=21402
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THE WIENER-KHINCHIN THEOREM FOR NON-WIDE SENSE ...
Index Terms— Non-wide Sense Stationary Processes, Power. Spectral Density, Subsampling, Wiener-Khinchin Theorem, Ban- dlimited. 1. INTRODUCTION ...
www.ece.iastate.edu/~luwei/wknonstat/NS_WK2.pdf
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Topic 7: Random Processes Random processes
Wide-sense stationary random processes. • X(t) is wide-sense stationary (WSS) if the following two properties both hold: mX(t) = m ∀t. RX(t1,t2) = RX(t2 − t1) ...
www.ece.mcgill.ca/~mvu5/ES150/7-sto_proc.pdf
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Approximation of Wide-Sense Stationary Stochastic Processes by ...
We restrict our analyses to Wide-sense stationary processes,. i.e., the class of ... about Wide-sense stationary processes, we refer to the standard literature, for ...
www.lti.ei.tum.de/fileadmin/w00bgd/www/pdf/05625620.pdf
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Stationary and Wide Sense Stationary Processes Definition: A time ...
chair. Estimation and Detection. Slide 1. Stationary and Wide Sense Stationary Processes. Definition: A time discrete stochastic process Θ[·] is called stationary ...
mns.ifn.et.tu-dresden.de/Teaching/Courses/EstDet_Documents/Stochastic_Signals.pdf
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Wide-sense stationary process 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 ...
[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 ...
Filtering of Wide Sense Stationary Quantum Stochastic Processes
Aug 6, 2007 ... Abstract: We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra.
[PDF]THE WIENER-KHINCHIN THEOREM FOR NON-WIDE SENSE ...
Department of Electrical and Computer Engineering, Iowa State University, Ames , IA. {luwei ... Index Terms— Non-wide Sense Stationary Processes, Power ...
[PDF]Lecture #17 Stochastic Process (3) Stationary Process Stationary ...
Kasetsart University, Bangkok, Thailand. 2. Stationary ... Definition: A stochastic process X(t) is stationary .... Theorem: For a wide sense stationary process. X(t), ...
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, ...
[PDF]SC505 STOCHASTIC PROCESSES Class Notes - MIT
Boston University .... 3.9 Power Spectral Density of Wide-sense stationary processes . ...... Thus, the random telegraph process is wide-sense stationary. Indeed ...
Filtering of Wide Sense Stationary Quantum Stochastic Processes ...
ABSTRACT We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power ...
[PDF]theorem for wide sense stationary processes
of wide sense stationary sequences, as soon as the random process with orthogonal .... be a family of (wide sense) stationary processes of complex ...... Goran Peskir, Department of Mathematical Sciences, University of Aarhus, Denmark, ...
Books on the term Wide-sense stationary process
Fundamentals of Applied Probability and Random Processes
Fundamentals of Applied Probability and Random Processes
Oliver Ibe, 2005
At a high level, it is a process whose statistical properties do not vary with time. In this book we consider only two types of stationary processes. These are the strict- sense stationary processes and the Wide-sense stationary processes.
Stochastic processes and their applications
Stochastic processes and their applications
Franck E. Beichelt, L. Paul Fatti, 2002
This book introduces stochastic processes and their applications for students in engineering, industrial statistics, science, operations research, business, and finance.
Probability, Statistics And Random Processes
Probability, Statistics And Random Processes
T. Veerarajan, 2002
A random process that is not stationary in any sense is called an evolutionary process. Two random processes (X(t)} and (Y(t)} are said to be jointly stationary in the wide sense, if each process is individually a WSS process and Rxv (/,, /2) is a ...
Numerical Solution of Stochastic Differential Equations
Numerical Solution of Stochastic Differential Equations
Peter E. Kloeden, Eckhard Platen, 1992
This means the process is only stationary with respect to its first and second moments. It is straightforward to show that a strictly stationary process is wide-sense stationary if its means, variances and covariances are all finite, but a wide- sense ...
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Wide-sense stationary process
Converting a Wide Sense CycloStationary process into a Wide Sense Stationary process
Converting a Wide Sense CycloStationary process into a Wide Sense Stationary process in Set Theory, Logic, Probability, Statistics is being discussed at Physics Forums
www.physicsforums.com/showthread.php?t=551000
Download Probability and random processes: using MATLAB with applications to continuous and discrete time systems ebook - Bonnie0127sedlak's blog
Probability and random processes: using MATLAB with applications to continuous and discrete time systems book download Donald G. Childers Download Probability and random processes: using MATLAB with applications to continuous and discrete time systems Herman, Noam Chomsky 1988 Pantheon Books ISBN10:0375714499;ISBN13:9780375714498. Solution Manual Electrical Engineering : Principles and Applications ....
mbnfchs.typepad.com/blog/2013/05/download-probability-and-random-processes-using-matlab-with-applications-to-continuous-and-discrete-time-systems-ebook.html
[1305.3376] Delay and Doppler Spreads of Non-Stationary Vehicular Channels for Safety Relevant Scenarios
arxiv.org/abs/1305.3376
stationary process | Classle
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Random Processes
2.2. Wide-Sense Stationary (WSS) ProcessesØ Mean of the random process X(t) is the mean of random variable X(t) at time instant t.∫+∞∞ −· dx x xf t X E t X) ( )] ( [) () ( )] ( [ t t X E Xµ ·Let fX(t)(x) be the pdf of X(t) at time instant t.
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MA1254 Random Processes Syllabus
text-align:right; float:right; MA1254 RANDOM PROCESSES 3 1 0 100 AIM This course aims at providing the necessary basic concepts in random processes. A knowledge of fundamentals and applications of phenomena will greatly help in the understanding of topics such a estimation and detection, pattern recognition, voice and image processing networking and queuing.
sourcecodesonline.blogspot.com/2011/01/ma1254-random-processes-syllabus.html
Stochastic Processes (GPS)
A stochastic process is a family of random variables indexed by a parameter for continuous-time stochastic processes orfor discrete-time stochastic sequences. For a deterministic signal such asthe value of x is determined by the value of t. Once t is
what-when-how.com/gps-with-high-rate-sensors/stochastic-processes-gps/
Average Power Spectrum Density | Engineering & Stuff
- A professional engineering blog. And the stuff ? everything else.
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