|WikiProject Systems||(Rated Start-class, Mid-importance)|
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- Yes, system A is time variant because it explicitly depends on t. Cburnett 03:32, 19 March 2006 (UTC)
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 22.214.171.124 (talk) 14:46, 18 May 2008 (UTC)
Notation in the "Abstract example" section
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
(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 Tr (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
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 xr: R→R by
xr(t) = x(t+r) for all t.
Now, for each r in R, consider an operator Tr: [function space]→[function space] defined by
Tr(x) = xr 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 ."
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)