Timeline for What Is Continuous White Noise in The Context of Signal Processing and Broadly
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 20, 2023 at 19:55 | comment | added | Royi | @TimWescott, It is so funny that we create camps here. EE + Physicist vs. Mathematicians. First, I'm pretty sure Physics people will use the Delta as a distribution, which is what it is. Moreover, when I did my EE I was also taught calculus of Distribution prior to the use of the Delta. There is only a single Math, the correct one. Indeed, you can either use White Noise model similar to what I linked or you go the Tempered Distribution path. You want simplicity, stick with arbitrary long support with constant value and arbitrary small correlation time. | |
| Aug 19, 2023 at 14:53 | comment | added | TimWescott | "...difference in understanding that engineers and physical scientists have with mathematicians about $\delta(t)$..." Or if not just that, then the fact that an engineer or physicist takes $\delta(t)$ to be a nice shorthand way of describing something physically impossible and is willing to ignore the 200 pages of exposition one (probably) needs to really nail down what it means, while those 200 pages of exposition are harder for a mathematician to ignore. I suspect that in the case of white noise there's another 200 pages to get from just what we mean by spectrally white to $\delta(t)$. | |
| Aug 19, 2023 at 12:00 | comment | added | Royi | @MarcusMüller, Have you read the reference? I think if you will, all your questions will be answered. Specifically that this is not a proper way to define a Random Process. | |
| Aug 19, 2023 at 11:57 | comment | added | Marcus Müller | @Royi why would one want to do that? What does deriving definition of the dirac function have to do with this? the statement stands as is; nobody expects it to be identical to the delta distribution | |
| Aug 19, 2023 at 9:23 | comment | added | Royi | I totally agree with the quoted definition: $ \text{ if } \forall {t}_{i} \neq {t}_{j} \; \mathbb{E} \left[ v \left( {t}_{i} \right) v \left( {t}_{j} \right) \right] = 0 \implies v \left( t \right) \text{ is a white noise } $. Now, can you derive this definition into the delta function based on this definition? | |
| Aug 19, 2023 at 5:48 | comment | added | robert bristow-johnson | The other funny thing is, Tim, is that I got the Papoulis book too. And although he mentions white noise a couple of times (pp 217 and 241), he really stays the hell away from the topic otherwise. That's disappointing. The college references that I am using is A.B. Carlson, Wozencraft and Jacobs, and Van Trees. Papoulis, normally very rigorous, doesn't wanna fuck with it. | |
| Aug 19, 2023 at 5:40 | comment | added | robert bristow-johnson | Tim, do you remember all the fuss that happened at comp.dsp when I was saying that whatever is the dimension of the argument of the dirac delta "function", the "value" of the function has the reciprocal dimension? And then all of the fuss that came from the math guys (the "distribution" description) and some EEs that just didn't get it at all? This is going to be like that, in fact, I think the root to the difference of understand of white noise comes directly from the difference in understanding that engineers and physical scientists have with mathematicians about $\delta(t)$. | |
| Aug 18, 2023 at 18:30 | comment | added | Royi | @MarcusMüller, Actually you can't :-). This is exactly the point of the question. The model we use in Signal Processing is not coherent Mathematically. There are ways to define it coherently, they require other tools. You may look at my answer and the reference I linked to which shows why you can't have both define the Auto Correlation with Delta and the Power Spectrum as constant and say they are a pair according to Wiener Khinchin Theorem. White Noise is a limit of process. There are some delicate way to work with it which is not a concern for Signal Processing but it is for other fields. | |
| Aug 18, 2023 at 18:13 | comment | added | Marcus Müller | @Royi why would you need to define a distribution? You don't! You can have nice gaussian white noise, but just as much uniform distributed. | |
| Aug 18, 2023 at 16:46 | comment | added | Royi | The trick is that the property of no correlation is not enough as we need to define a distribution. It is a bit tricky as if you go one path starting with only no correlation you get some "paradoxes". | |
| Aug 18, 2023 at 16:05 | history | answered | TimWescott | CC BY-SA 4.0 |