Talk:Time-invariant system

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I know nothing about this topic, but I wanted to draw attention to this edit. Can someone please check the accuracy of this change? --Wolf530 00:55, 19 March 2006 (UTC)[reply]

Yes, system A is time variant because it explicitly depends on t. Cburnett 03:32, 19 March 2006 (UTC)[reply]

i take it that shift invariant system are the exact same thing as time invariant systems? Could someone with an account add a link from shift-invariant? —Preceding unsigned comment added by 92.73.83.53 (talk) 14:46, 18 May 2008 (UTC)[reply]

I don't know how to type fancy math symbols, so I apologize for that in advance. As for the main issue...

Are the "δ" and "*" in

${\displaystyle x(t+1)=\,\!\delta (t+1)*x(t)}$ (first equation in the "Abstract example" section)

widely-understood notational conventions? If they're not, then I'd suggest defining them explicitly. I can only speak for myself, but I tried for ten minutes to think of a sane interpretation of "δ" and "*" before I gave up and decided to simply define the whole string of symbols δ(t+r) to be the shift operator T_r (for each r), and the * to be function composition, under the assumption that someone neglected to put parentheses before "δ" and after "x" -- i.e., that the original writer meant

"x(t+1) = (δ(t+1)*x)(t)."

If there's some notational convention that I'm not aware of -- and that may very well be the case, because I am far from being an expert on the subject (case in point: I had to look up "Time-invariant system") -- then you're welcome to ignore this post. Otherwise, in my very humble opinion, it would be great if someone would rewrite that part so as to omit the line

${\displaystyle x(t+1)=\,\!\delta (t+1)*x(t)}$

entirely. I don't have time to rewrite it myself (as that would involve learning how to write math-y stuff on here), but as a rough sketch, I suggest something along the lines of

____________________________________

"Given any function x in [whatever function space] (optional) and any r in R, define x_r: R→R by

x_r(t) = x(t+r) for all t.

Now, for each r in R, consider an operator T_r: [function space]→[function space] defined by

T_r(x) = x_r for all x in [function space]."

____________________________________

Now that I think about it, if you clean that up a bit, I think it could replace everything before the line

"Suppose we represent a system by an operator ${\displaystyle \mathbb {H} }$."

in the "Abstract example" section.

(Also -- again, in my humble opinion -- some people severely underestimate how helpful it is to explicitly mention domains and codomains when they're defining or discussing functions. The writer may think that this is unnecessary, and yes, it may make the text a little bit longer than it actually has to be, but I, personally, find it so much easier to follow mathematical writing if I don't have to stop and figure out "what's taking what to what," so to speak. That's a huge drain on cognitive resources that could otherwise be spent concentrating on the main ideas.)

Usewhosename (talk) 02:51, 20 October 2015 (UTC)[reply]

In the main section "Time-invariant system" I quote : "If a system is time-invariant then the system block commutes with an arbitrary delay." "commutes" takes us to a page that does not explain system block commutation, I mean how system blocks are commuted ? Unclear. Then after I went to read the abstract example I kind of understood it. A small image won't hurt in the Abstract example though to illustrate the block idea. Anyway, in the main section I suggest it becomes something like : I quote : "If a system is time-invariant then the system block commutes with an arbitrary delay, as described below." Where the word "below" referring to the abstract example section : https://en.wikipedia.org/wiki/Time-invariant_system#Abstract_example And where we remove the link from "commutes" since it is already there in the Abstract example section.

The current version of the article has three sections titled Simple example, Formal example and Abstract example. Wikipedia is an encyclopedia, not a textbook, and as such it shouldn't be treated as a textbook including examples solved step by step. Therefore, I propose to remove those sections. Yes, the article will become shorter, but at least it will be more consistent with Wikipedia's guidelines.

What I think we can do is add example relations of systems that are time-invariant. So, instead of proving whether a system is time-invariant or not (as the current version of the article shows), we can just say something like "systems described by the equations ${\displaystyle y(t)=x^{2}(t)}$ and ${\displaystyle y(t)=\cos {(x(t))}}$ are time-invariant", and add references.

If no-one opposes to my suggestion, I'll be bold. --Alej27 (talk) 22:17, 30 June 2021 (UTC)[reply]