Talk:Discretization

Hello, I am unsure but I think there is an error in the section to calculate the discretization of a continuous system. In the very last step in the process one simplifies $\backslash int\_0^T\; e^\{Av\}dv$ by using $A^\{-1\}(e^\{AT\}\; -\; I)$. As far as I can tell this is not correct in general. Assume the system contains an integrator and the matrix $A$ has therefore an eigenvalue at zero. Thus $A$ is not regular and $A^\{-1\}$ does not exist. Nevertheless such systems exist and can for sure be discretized.

I tried to get through it myself but did not yet succeed. Maybe someone here knows already the solution and is willing to document it here. Please let me know if I can help doing it. --Clupus (talk) 13:35, 20 February 2015 (UTC)

Hello,

I think I have provided some information that help "solving" the problem when $A$ is singular. Best. --Sumo Hanoi (talk) 14:45, 2 February 2021 (UTC)

Is the point list in the lead meant to be there? It doesn't seem like it is; it just appears completely without explanation or context. If it is meant to be there, we need to make it clear how it fits in. —Kri (talk) 12:47, 1 February 2016 (UTC)

Per WP:Technical, I think it is possibly too technical and laden with linguistics jargon, especially since the article is already quite technical (albeit in a different field). I tried to simplify the phrasing somewhat, but I think adding a sentence more explicitly explaining the difference in connotations might be helpful.

That said, I would need some help understanding the actual difference in connotation between the two terms. Cheers! Scientific29 (talk) 18:54, 13 January 2018 (UTC)

:– On the one hand I'd say that you exclusively discretize the continuous time into discrete time. On the other hand, in information theory, you can quantizate any quantity (say a measure of temperature or a voltage) over a finite number of bytes, the space-continuous evolving quantity is represented by a finite set of values ('00','01','10','11' with two bytes). see https://en.wikipedia.org/wiki/Quantization_(signal_processing) — Preceding unsigned comment added by NonLynSys (talk • contribs) 15:51, 22 January 2018 (UTC)

The units don't seem correct given the rest of the analysis, and the source in the textbook defines the state noise w differently, so I think there might've been an error in translating that source to this page. 128.244.42.15 (talk) 16:43, 9 March 2023 (UTC)

Someone long ago asked in the talk page what would be the "opposite" process of discretization here, and not a single person bothered to provide a response. I want to provide one today: isn't interpolation a form of an inverse process?

Interpolation takes a set of discrete points and constructs a larger set of data, typically a continuous curve, that incorporates those points. Discretization takes a continuous entity and approximates it with a discrete collection of points. Sources that talk about interpolation and discretization together include [https://link.springer.com/chapter/10.1007/978-3-211-71576-5_3 The Boundary Element Method with Programming] and [https://www.cambridge.org/core/books/abs/finite-elements/frontmatter/A8ED9A5D4DB84E73646CC2EB676D04C0 Finite Elements: Theory and Algorithms].

I find it baffling. I do not see one term anywhere on the article for the other. Likewise, unless I go to really catch-all umbrella articles such as numerical analysis or continuous or discrete variable, it is very hard to find an article that contains both terms - relevant pages such as smoothing, curve fitting, or digital signal processing only contain one and not the other. (Same goes for their talk pages.) Therefore, I took the time to add each other in the respective "see also" sections. 2600:1012:A023:7497:B104:8626:7D0C:3983 (talk) 04:44, 20 November 2024 (UTC)