Timeline for What Is Continuous White Noise in The Context of Signal Processing and Broadly
Current License: CC BY-SA 4.0
34 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 19, 2023 at 14:51 | comment | added | Marcus Müller | … exist, just that WKT is not useful to work with it. That's a fine observation, but that doesn't mean at all that the process (e.g. the Dichotomous White Noise from section III) is not white, or that the definition of white used here is not useful, or anything. Only that WKT has its prerequisites not fulfilled. | |
| Aug 19, 2023 at 14:48 | comment | added | Marcus Müller | @Royi I don't feel like nitpicking vocab, really, but here I'm really just a bit confused (that's not your fault, the paper is a bit sloppy on that; it states a form of the theorem in (11), but omits the conditions, or much worse, says "It can then be shown that …", without actually requiring the conditions before.). Anyway, the argument from that paper is: Either a theorem is false, or all the things that fulfill its conditions obey it. So, if the statement of a true theorem does not apply to something, then its prerequisites must not be met. But that does not imply such a process doesn't… | |
| Aug 19, 2023 at 13:38 | comment | added | Royi | @MarcusMüller, The paper show the pair of delta defined with Auto Correlation and Constant Frequency can not obey the Wiener Khinchin Theorem. Did we establish that? | |
| Aug 19, 2023 at 13:23 | comment | added | Marcus Müller | @Royi yep, the author uses the definition $R(\tau) = k \delta(\tau), G(f) = \eta/2$; fine by me, but your initial answer's sentence is explicitly restricting the condition to $G(f)$; now I'm fully confused by the statement of your answer. | |
| Aug 19, 2023 at 13:18 | comment | added | Marcus Müller | then I don't understand your words, which stand – verbatim – as "A more rigorous derivation can be done by defining the (Gaussian) White Noise as the derivative of Wiener Process.". Because that definition is in stark conflict with the paper. It's not "more rigorous", it's contradicting. | |
| Aug 19, 2023 at 13:18 | comment | added | Royi | @MarcusMüller, The comment about continuous noise being Gaussian is "I think.". I will look into that. Now that you have read the paper, you see one can define white noise coherently? You may also look on other papers of the same writer on the subject. | |
| Aug 19, 2023 at 13:17 | comment | added | Royi | @MarcusMüller, You're mixing my words. Th paper is about what's needed to have a valid stationary white noise. | |
| Aug 19, 2023 at 13:14 | comment | added | Marcus Müller | generally, I'm a bit confused about how you're reading from the paper that white noise is going to be Gaussian: the whole point of III is that a very non-Gaussian distributed random process is white. Is the problem you have with that that it only applies for arbitrary small, but non-zero correlation lags? | |
| Aug 19, 2023 at 13:03 | comment | added | Marcus Müller | (found a mistake in my criticism of the math of your paper, so will have to postpone) | |
| Aug 19, 2023 at 12:12 | history | edited | Royi | CC BY-SA 4.0 | added 1356 characters in body |
| Aug 19, 2023 at 11:56 | comment | added | Royi | @MarcusMüller, I don't get it. My answer gives a reference which defines White Noise well. In a manner which both obeys all properties needed for the Signal Processing context and it is well defined Mathematically. It is the answer to the question. If there are others, I will mark them. But they have to be a valid Random Process which obeys the properties of Random Processes. Specifically Stationary. | |
| Aug 19, 2023 at 11:52 | comment | added | Marcus Müller | as said, that's a whataboutism. You are trying to make it now my job to provide something better, where it would be this answer's job to be sensible. It's not my job. | |
| Aug 19, 2023 at 11:51 | comment | added | Royi | @MarcusMüller, Why not? I gave you one on the reference. It works in the Signal Processing context and in the Mathematical context. Have you read the reference I point to? | |
| Aug 19, 2023 at 11:50 | comment | added | Marcus Müller | @Royi please don't whataboutism me: this answer is plain not coherent nor a common definition. The presence of a coherent definition in another answer has no bearing on that :) | |
| Aug 19, 2023 at 11:50 | comment | added | Marcus Müller | …restricting your definition is as I wrote this comment. The question asks for "coherent definitions" as "used in signal processing"; and this answer's neither. Please don't take this personally!) | |
| Aug 19, 2023 at 11:49 | comment | added | Royi | @MarcusMüller, Coherent in the Mathematical way. Can you give me one which doesn't have a coherent Mathematical model? | |
| Aug 19, 2023 at 11:46 | comment | added | Marcus Müller | @Royi no, it's not a coherent way, sorry! That's an extremely limiting definition that excludes a lot of very white processes. That's what I meant above: you make an arbitrary restriction ("white noise is defined as derivative of a Wiener process"), then come to a conclusion ("hence, white processes are Gaussian"). I can also say "white noise is the sound a cat makes when being very content about being petted" and then come to conclusions "if there's white noise, a cat is being petted somewhere close". But that would obviously a fallacy! (I'm the second -1 now, because I just realized how… | |
| Aug 19, 2023 at 11:36 | comment | added | Royi | @MarcusMüller, On top of that, I think you can't have non Gaussian continuous white noise. But this is for a different discussion. | |
| Aug 19, 2023 at 11:35 | history | edited | Royi | CC BY-SA 4.0 | added 11 characters in body |
| Aug 19, 2023 at 11:34 | comment | added | Royi | Could the ones who -1 leave some comment please? | |
| Aug 19, 2023 at 11:33 | comment | added | Royi | @MarcusMüller, I made no such claim. Brownian Motion can be defined on its own with no relation to white noise. On the contrary, a coherent way to define White Noise is by using Wiener Process. Also the connection is only with Gaussian White Noise. | |
| Aug 19, 2023 at 9:36 | comment | added | Marcus Müller | Royi, dangerous claim that just because the integral of a WGN process is a Brownian process, that every white process must be the derivative of a Brownian process. As my house mathematician would say, "your theorem leaves room for exceptions", which I've been assured is a good way to start an exchange of loud words in a mathematician's conference. I'm still looking forward to one day witnessing such a thing happening, though. | |
| Aug 19, 2023 at 5:58 | comment | added | Royi | @robertbristow-johnson, Let's stop. You're not into a dialogue. | |
| Aug 19, 2023 at 5:45 | comment | added | robert bristow-johnson | Royi, do you know what a strawman is? | |
| Aug 19, 2023 at 5:43 | comment | added | Royi | @robertbristow-johnson, Also, If you're so sure about your model, I asked you, can you build me a White Noise which has an Exponential distribution? | |
| Aug 19, 2023 at 5:38 | comment | added | Royi | @robertbristow-johnson, Also, Why -1? Is there anything not accurate in the answer? I'd be happy to fix it. | |
| Aug 19, 2023 at 5:37 | comment | added | Royi | @robertbristow-johnson, Physicists actually don't use the same definition. Again, there are Math laws. If you want the transform from the Auto Correlation to the Power Spectrum, to be Mathematically reasonable there are rules of integration to work by. It has nothing to do with Physicists or Engineers. It has to do with Math. The reason Signal Processing gets away from this is that we don't have a real interest in the Math beast of White Noise, we only care about what happens when it goes through a Linear System with limited bandwidth. | |
| Aug 19, 2023 at 5:33 | comment | added | robert bristow-johnson | @Royi, this is going to boil down to the same difference in understanding that engineers (and physicists) have with $\delta(t)$ (and treat it as a "function") in comparison to the rigorous mathematical treatment (that makes it into a "distribution" and not a function). We engineers are comfortable with treating the dirac impulse as a special function. If you, somehow, come to a conclusion that "band-unlimited white noise has a variance", then whatever you're talking about is different than what we are talking about. White noise has finite variance only when there is a bandwidth. | |
| Aug 19, 2023 at 5:27 | comment | added | robert bristow-johnson | I would, instead, define the Wiener Process (what we Neanderthal electrical engineers call "Brown noise" or "Red noise") as the integral of white noise. And this brown noise has infinite variance, too, (or, at least, grows without bound) if you wait long enough. | |
| Aug 19, 2023 at 5:17 | comment | added | Royi | @TimWescott, Wiener Process is the distribution of Brownian Motion. A Physical phenomenon which needs no definition of White Noise in order to be defined. Look on the Wikipedia term of Wiener Process, it has a definition. I don't see White Noise there. | |
| Aug 19, 2023 at 5:14 | history | edited | Royi | CC BY-SA 4.0 | added 58 characters in body |
| Aug 18, 2023 at 19:21 | comment | added | TimWescott | Yet, I've only ever seen the Wiener process defined as the integral of white noise. | |
| Aug 18, 2023 at 16:52 | history | edited | Royi | CC BY-SA 4.0 | added 2 characters in body |
| Aug 18, 2023 at 16:44 | history | answered | Royi | CC BY-SA 4.0 |