# Talk:Discretization

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--213.224.27.206 (talk) 09:43, 17 January 2012 (UTC)== Extra == It would be useful if this article also covered discritizing stochastic differential equations for sampling.

Absolutely! Please contribute if you are familiar with the subject. :-) --Fredrik Orderud 22:56, 17 August 2006 (UTC)

There is minor ambiguity by using T for the sampling time as in Qd the matrix Transpose also uses the T symbol.

Tustin(bilinear) is not an approximation but rather an exact transformation or mapping if you like... 24 March 2009 —Preceding unsigned comment added by 131.180.28.210 (talk) 15:20, 24 March 2009 (UTC)

Is there a name for the opposite of discretization? "to make something consisting of discrete parts into a continuous entity"? —Preceding unsigned comment added by 71.67.248.185 (talk) 00:32, 28 June 2010 (UTC)

In my opinion "continuous zero-mean white noise" is not realistic. A noise is white over a finite bandwidth otherwise noise energy goes to infinity....

## Approximations section

Under the "Approximations" section, could someone (I'll maybe do it when I have some free time) please add the scaling-and-squaring method to approximate matrix exponentials? (for more info, see SIAM J. MATRIX ANAL. APPL. Vol. 26, No. 4, pp. 1179–1193, "The Scaling and Squaring method for the matrix exponential revisited.") XWolfRH (talk) 17:18, 10 April 2012 (UTC)

## in the "Discretization of linear state space models" section

I was wondering about the statement "where v and w are continuous zero-mean white noise sources with covariances..." Everything that I have been reading (and I am relatively new to stochastic processes and Kalman filters) says that the covariances of continuous-time white Gaussian noise processes are infinite, stemming from the Dirac delta function in the definition of the autocorrelation function. This would apply to the covariance matrix as well. On the other hand, the power spectral density matrix is finite. My questions are: 1) are Q and R for the continuous-time noises really the PSD matrices and not covariance matrices? 2) If so, does this change the equations and/or procedure for finding the discrete-time version Qd in the "Discretization of process noise" section? Thanks, 68.83.8.55 (talk) 03:57, 26 September 2012 (UTC) Ray K.

## 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 ${\displaystyle \int _{0}^{T}e^{Av}dv}$ by using ${\displaystyle A^{-1}(e^{AT}-I)}$. As far as I can tell this is not correct in general. Assume the system contains an integrator and the matrix ${\displaystyle A}$ has therefore an eigenvalue at zero. Thus ${\displaystyle A}$ is not regular and ${\displaystyle A^{-1}}$ 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)

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

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

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

to a smooth regular function ${\displaystyle f(t)}$ that is not growing faster than polynomials, where ${\displaystyle \delta (t)}$ is the Dirac delta and ${\displaystyle T}$ is a positive, real increment between consecutive samples ${\displaystyle f(kT)}$ of function ${\displaystyle f(t)}$. The generalized function ${\displaystyle {\bot \!\bot \!\bot }_{T}f}$ is also called the discretization of ${\displaystyle f}$ with increments ${\displaystyle T}$ or discrete function of ${\displaystyle f}$ with increments ${\displaystyle T}$. 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.

## 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.wikipedia.org/wiki/Quantization_(signal_processing)