Timeline for When deriving the power spectral density of stochastic processes, why does taking an expectation allow the $T\rightarrow\infty$ limit to be taken?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 8, 2020 at 11:22 | vote | accept | teeeeee | ||
| Apr 8, 2020 at 9:22 | answer | added | jithin | timeline score: 0 | |
| Apr 8, 2020 at 7:55 | answer | added | Matt L. | timeline score: 3 | |
| Apr 8, 2020 at 7:17 | comment | added | teeeeee | Possibly, something like that could make sense to me, but I haven't seen anything like that in any other derivation. I am learning this for the first time, so feel like I'm just missing something. What you said about it blowing up is what I was thinking - if the individual realisations of $X_T$ are not defined in the limit, I don't see what would be so different about the expectation of many. What happens for example if you coincidently obtain all ideantical spectra for every realisation - the expectation should do nothing in that case, i suppose. | |
| Apr 8, 2020 at 3:47 | comment | added | Dan Boschen | I think I see your point; and would there need to be an additional requirement that $|X_T(f)|^2$ would need to be ultimately decreasing at the rate of $1/f$ or more as $f -> \infty$ otherwise the Expectation integral blows up, right? | |
| Apr 7, 2020 at 23:27 | history | edited | teeeeee | CC BY-SA 4.0 |
added 13 characters in body
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| Apr 7, 2020 at 23:11 | history | edited | teeeeee | CC BY-SA 4.0 |
edited title
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| Apr 7, 2020 at 22:47 | history | asked | teeeeee | CC BY-SA 4.0 |