Talk:Discretization

Error in section "Derivation"

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 $\int _{0}^{T}e^{Av}dv$ 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)

Discretization of a function

I can find no reliable sources that discuss the following as "discretization of a function", let alone that this is what it means "In mathematics". That seems like WP:OR to me. I would be perfectly willing to restore it, if it can be appropriately sourced, and "In mathematics" is replaced by whatever seems most appropriate ("in sources like XXX..." maybe).

In mathematics, the discretization of a function is the operation ${\bot \!\bot \!\bot }_{T}$ that assigns the generalized function ${\bot \!\bot \!\bot }_{T}f$ defined by

$({\bot \!\bot \!\bot }_{T}f)(t)\,{\stackrel {\mathrm {def} }{=}}\,\sum _{k=-\infty }^{\infty }\,f(kT)\,\delta (t-kT)$

to a smooth regular function $f(t)$ that is not growing faster than polynomials, where $\delta (t)$ is the Dirac delta and $T$ is a positive, real increment between consecutive samples $f(kT)$ of function $f(t)$. The generalized function ${\bot \!\bot \!\bot }_{T}f$ is also called the discretization of $f$ with increments $T$ or discrete function of $f$ with increments $T$. Discretization is an operation that is closely related to periodization via the Discretization-Periodization theorem. Example: Discretizing the function that is constantly one yields the Dirac comb.

Sławomir Biały (talk) 11:55, 16 May 2015 (UTC)

Stray point-list

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)

Explanation of difference between "discretization" and "quantization"

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.wiki.x.io/wiki/Quantization_(signal_processing) — Preceding unsigned comment added by NonLynSys (talk • contribs) 15:51, 22 January 2018 (UTC)

Is Q really the power spectral density of the process noise?

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)