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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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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1answer
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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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1answer
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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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1answer
31 views
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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1answer
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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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1answer
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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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1answer
113 views
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 ...
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1answer
192 views
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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4answers
854 views
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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2answers
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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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What is a good example of an ergodic process?
I'm trying to find simple examples of an ergodic process. What process comes to your mind as a good illustration of its properties?
A quick research (Wikipedia, another answer) mainly gives examples ...
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1answer
230 views
Ergodicity of joint process
If we have two processes and both of them are ergodic. Does this mean that the joint proces is ergodic? Or other way around? If we have the dynamics for both components of the joint process what are ...
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1answer
438 views
Is ergodic in mean a property defined only for WSS stochastic processes?
I understand the definition of a random process $X(t)$ being ergodic in mean (first-order ergodic) is that the expectation of the sample mean $<u_X>_T=\frac{1}{T} \int_{\frac{-T}{2}}^{\frac{T}{2}...
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1answer
241 views
WSS Ergodic Process with Power Spectrum
I was given a WSS ergodic process $x(t)$ with power spectrum :
$$
\begin{array}{rcl}
G_x(f) &=&1−\left|\frac{f}{B}\right| &\mbox{for } |f|<B\\
G_x(f) &=& 0 & \...
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1answer
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Understanding Ergodicity and Ensemble Averaging
Literature says that a stationary signal is ergodic, if its ensemble average = time averages. Should it be the statistics computed by time averaging = statistics computed by ensemble averaging?The way ...
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0answers
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How to show that an ergodic process must be a strict-sense stationary one? [duplicate]
I have trouble to distinguish these two concepts namely ergodic process and strict-sense stationary process. I look at one of the books about the signal processing that says an ergodic process must be ...
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6answers
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What is the distinction between ergodic and stationary?
I have trouble distinguishing between these two concepts. This is my understanding so far.
A stationary process is a stochastic process whose statistical properties do not change with time. For a ...
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2answers
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Does the determination of the ergodicity of a signal force any changes in methodology?
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. -from wikipedia
From the perspective ...
