Questions tagged [ergodic]
In mathematics, the term ergodic is used to describe a dynamical system which, broadly speaking, has the same behavior averaged over time as averaged over space.
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Aren't ergodicity and stationarity the same?
I have read this questions 1, 2. In the first one, they have the same question as I do, but the answers don't really ressolve the issue. I understand stationarity in terms of simulation, sampling and ...
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1 answer
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Ergodicity clarification
On page 201 of https://stanford.edu/~dntse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter5.pdf, it is mentioned that This observation suggests that the capacity result (5.89) holds for a ...
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If $X(t)$ is a WSS process with mean 5, what is the mean of $X(2t)$? [closed]
I know mean is constant for a WSS process but I am still confused about the mean for this process. My process was by integrating $X(2t)$ from $0$ to $T$, then substituting $t′=2t$. So the limits ...
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When is the Correlation Coefficient Ergodic
Given Wide Sense Stationary (WSS) processes X and Y that are ergodic to the mean and autocovariance. Under what conditions is the correlation coefficient ergodic to the mean? ie: $lim_{T->\infty} \...
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1 vote
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Does the convergence rate never increase of a Stationary Ergodic Random Processes under downsampling?
Summarize the problem Given A Stationary Random Processes (strict sense) $X_i$ I define two Stationary Ergodic Random Processes by $$ \bar{X}_n = \frac{1}{n} \sum_{i=0}^{n-1} X_i \ \ \text{and} \ \ \...
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2 answers
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Intuitive definition of ergodicity for random signal
Is it possible to define the ergodicity of the random signal in an intuitive sense without using any statistical reference?
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1 answer
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A check on the definition of the continuous periodogram, and does it assume ergodicity somewhere?
Can someone verify my understanding of what the continuous periodogram is/means, and please tell me if I say something wrong: As I've learned so far, the power spectral density of a wide-sense ...
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1 vote
1 answer
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Why the requirement of the GCD of the lengths of all circuits in the graph being one?
I am reading A Mathematical Theory of Communication. The second requirement of an ergodic process confuses me (emphasis mine): All the examples of artificial languages given above are ergodic. This ...
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2 votes
1 answer
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Autocorrelation of a uniform random process
i am currently learning the basics of signal processing. As you may know the definition of the autocorrelation is different if you look at a random process or for example a deterministic signal My ...
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1 answer
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Assessing relative wireless channel quality using Capacity and Condition Number CDFs
I have Channel capacity analysis figures for two wireless channels show below: My question: While ergodic capacity in the first subplots are very clear in conveying the channel capacity, How to make ...
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1 vote
1 answer
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Question regarding AC power of ergodic process
We know Ergodic process is the subset of Weakly stationary process which permits us to substitute time average for ensemble Average My teacher said If $X(t)$ is Ergodic random process then following ...
user33321
3 votes
1 answer
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Second moment ergodicity of gaussian random process
How can I prove that a WSS Gaussian stochastic process with mean 0 is mean-square ergodic in the second moment if and only if: $$\lim_{n \to \infty} \frac{1}{n}\sum_{k=0}^n r_{xx}^2(k) = 0$$ When $...
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Is the output of function of two ergodic processes ergodic?
Let $\{\xi_k\}_{k\in \mathbf{Z}}$ and $\{\epsilon_k\}_{k\in \mathbf{Z}}$ be two independent zero-mean Gaussian processes (i.i.d.). Is the output of the function $f$ such that $y = f(\dots,\xi_{k-1},\...
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4 votes
4 answers
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Can this be considered wide sense stationary?
I was discussing this problem with one of my classmates. The picture shows a recording of the heart rate during before and after sleep. Can the whole process be considered wide sense stationary? (I ...
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4 votes
2 answers
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What's the meaning of ergodicity? [duplicate]
I just read the topic about Ergodicity but I have ambiguity about its meaning (by intuition). What does mean: (for mean) Statistical average = Time average. Could you please explain it in detail. ...
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