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.
The article Wide-sense stationary process at en.wikipedia.org was accessed 47 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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Stationary and Wide Sense Stationary Processes
Stationary and Wide Sense Stationary Processes Guy Lebanon January 6, 2006 Definition 1. A RP X = {X t: t ∈ R} or X = {X n: n = ...,−2,−1,0,1,2 ...
www.cc.gatech.edu/~lebanon/notes/stationarity.pdf
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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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• 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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Signals, Systems and Inference, Chapter 9: Random Processes
chapter we define random processes via the associated ensemble of signals, and be ..... (ti − tj ), then the process is said to be wide-sense stationary (WSS).
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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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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Topic 7: Random Processes Random processes - iSites
Stationary processes and ergodicity ... A random process, also called a stochastic process, is a family of random .... Wide-sense stationary random processes.
isites.harvard.edu/fs/docs/icb.topic133498.files/7-sto_proc.pdf
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Solutions to HW12 Problem 10.10.2 • Problem 10.10.2 Solution
Apr 27, 2006 ... Is Y (t) = A + X(t) a wide sense stationary process? Problem 10.10.2 Solution. To show that Y (t) is wide-sense stationary we must show that it ...
www.engr.iupui.edu/~skoskie/ECE302/hwCsoln_06.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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Lecture 25 — April 12 25.1 Outline 25.2 Wide-sense Stationarity
25.2 Wide-sense Stationarity. The model we are using for random signals is that they are wide-sense stationary (WSS). This term has two parts to its meaning:.
www-inst.eecs.berkeley.edu/~ee123/sp07/lectures/lec25_scribe_battaglia.pdf
Search results for "Wide-sense stationary process"
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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 ...
Stationary process - Wikipedia, the free encyclopedia
Any strictly stationary process which has a mean ... The main advantage of wide-sense stationarity is ...
[PDF]Chapter 6: Random Processes1 - Yunghsiang Sam Han
random variable. Graduate Institute of Communication Engineering, National Taipei University ...... Stationary random process → Wide-sense stationary process.
[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.
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. College of .... 3.9 Power Spectral Density of Wide-sense stationary processes . ... 4.6 Ergodicity of Stationary Random Processes .
[PDF]Chapter 4 Random Processes
Nov 25, 2012 ... Random Processes. Xidian University .... 4.3.2 Properties for Wide Sense Stationary Random Processes ....................................................10.
[PDF]Problem Set 9 w/ soln - Winlab
THE STATE UNIVERSITY OF NEW JERSEY. RUTGERS ... Consider a random process X´tµ defined by ... The process Z´tµ is hence wide sense stationary.
Filtering of Wide Sense Stationary Quantum Stochastic Processes ...
University of Wales, Aberystwyth, Ceredigion, SY23 3BZ, Wales Abstract We introduce a concept of a quantum wide sense stationary process taking values in a ...
[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.
Books on the term Wide-sense stationary process
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.
Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers
Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers
2004
This user-friendly resource will help you grasp the concepts of probability and stochastic processes, so you can apply them in professional engineering practice. The book presents concepts clearly as a sequence of building blocks that are identified either as an axiom, definition, or theorem. This approach provides a better understanding of the mat...
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, ...
Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers
Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers
Roy D. Yates, 2014
This text introduces engineering students to probability theory and stochastic processes. Along with thorough mathematical development of the subject, the book presents intuitive explanations of key points in order to give students the insights they need to apply math to practical engineering problems. The first seven chapters contain the core mate...
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 ...
Theory of Probability and Random Processes (Universitext)
Theory of Probability and Random Processes (Universitext)
2012
A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It provides a comprehensive and self-contained exposition of classical probability theory and the theory of random processes. The book includes detailed discussion of Lebesgu...
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 ...
Schaums Outline of Digital Signal Processing, 2nd Edition (Schaum's Outline Series)
Schaums Outline of Digital Signal Processing, 2nd Edition (Schaum's Outline Series)
2011
The ideal review for your digital signal processing course More than 40 million students have trusted Schaum’s Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum’s Outlines cover everything from math to science, nursing to language. The main feature for all these books is ...
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Blog posts on the term
Wide-sense stationary process
Stationary process - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Stationary_process
Spectral factorization of wide sense stationary processes on Z2
www.sciencedirect.com/science/article/pii/0047259X86900928
Multiplicity theory for multivariate wide sense stationary generalized processes
www.sciencedirect.com/science/article/pii/0047259X75900500
• Strict and Wide Sense Stationarity • Autocorrelation Function of a ...
opencourses.emu.edu.tr/mod/resource/view.php?id=170&redirect=1
stochastic calculus - About stationary and wide-sense stationary processes - Mathematics Stack Exchange
math.stackexchange.com/questions/540055/about-stationary-and-wide-sense-stationary-processes
probability - wide sense stationary process - Mathematics Stack Exchange
math.stackexchange.com/questions/994716/wide-sense-stationary-process
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
Different definitions of ergodicity for stationary processes - MathOverflow
mathoverflow.net/questions/156201/different-definitions-of-ergodicity-for-stationary-processes
X(t) Is A Wide Sense Stationary Random Process ... | Chegg.com
Answer to X(t) is a wide sense stationary random process with expected value E[X(t)] = 1 and autocorrelation function RX(tau) = 2-...
www.chegg.com/homework-help/questions-and-answers/x-t-wide-sense-stationary-random-process-expected-value-e-x-t-1-autocorrelation-function-r-q1765793
stationary process | Classle
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