What is a Stationary Random Process?
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- Опубліковано 19 бер 2023
- Explains the concept of stationarity in random processes, using an example and diagrams.
* Note that I unfortunately forgot to mention that Stationarity also requires that the joint distribution of X(t1) and X(t2) is the same as the joint distribution of X(t1+Δ) and X(t2+Δ), for any t1, any t2, and for all Δ. In summary, this means that the way in which X(t1) and X(t2) are related, is the same as the way in which X(t1+Δ) and X(t2+Δ) are related. In other words, the level of dependency between two values that are spaced Δ apart, doesn't change over time. Or from yet another perspective, how independent they are from each other, doesn't change over time.
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thanks Professor, even if I have some prior knowledge, your videos help me to rewire my brain.
That's great. I'm so glad they help.
Really appreciate how you show things visually!
I'm glad you like the approach.
Thank you Professor. Waiting for more videos about statistical analysis of random processes
I'm glad you like the videos. Are there any specific topics you'd like me to cover on Random Processes?
@@iain_explains Please make a video about a system which is stationary in time average and a system which is stationary in ensemble average , and ergodicity.
I've got a video coming up on this topic, in the next couple of weeks.
@@iain_explains Thank you Professor.
More generally, for a stationary process, the joint distribution of X(t1)
and X(t2) is the same as the joint distribution of X(t1+Δ) and X(t2+Δ).
In particular, if a process is stationary, then its analysis is usually simpler as the probabilistic properties do not change by time.
Thanks for this. Yes, I forgot to mention the joint distributions. That's a pain. I was mostly thinking about the relationship between stationarity and ergodicity (which someone had asked me about). I'll add a note to the description below the video. Thanks again!
Under rated gem 💎
I'm glad you like the channel.
Hello Professor, thanks for the video. I have a question. Is it sufficient to say that a random variable is stationary if it looks like white noise when plotted against time?
Thanks in advance!
No, it's not sufficient to just look at the waveforms. Also, it might be that there is time-correlation between the samples, but the RP can still have the same probability distribution at all times (and hence it is stationary, but doesn't look like "white noise"). More details are in these videos: "Are Stationary Random Processes Always Ergodic?" ua-cam.com/video/onxzu2xUQ4E/v-deo.html and "What is Autocorrelation?" ua-cam.com/video/hOvE8puBZK4/v-deo.html
Could you do a video on how to construct the PDF? It makes intuitibe sense but I am having a hard time actually making it.
I'm not sure what you mean by the phrase "how to construct". Have you seen my video: "What is a Probability Density Function (pdf)?" ua-cam.com/video/jUFbY5u-DMs/v-deo.html
Question: By saying that the PDFs of the two RV are the same that does that mean the variance and the mean are the same? Or does it mean that the PDFs are either both Rayleigh or both Gaussian?
It means they are the same. ... Since they are the same, then yes, they will have the same mean, the same variance, the same distribution, the same everything ... because they are the same.
Thanks a lot@@iain_explains
If I understood correctly, this means the process PDF does not depend on time? Perhaps "static" random process would have been be a more appropriate when the term was being coined :-).
I'm not so sure about which term is better, ... and I wasn't even alive when the term was being coined ... 🤔😁
Does the fact that stationarity happen for short recording time play an important role in DSP ?
Sorry, I'm not sure what you're asking.
@@iain_explains I mean " do a lot of DSP algorithm can only work if stationary hold ?"
Most DSP algorithms assume stationarity of noise processes. But it depends on which DSP algorithms we're talking about, whether they assume stationarity of the `signal' component too.
@@iain_explains oh thank you there is so much subtlety