The formula stated here:
https://en.m.wikipedia.org/wiki/Periodic_summation
is not clear for me what the point of such a formula is and if i interpret it correctly.
For me, the only "natural" i.e. direct interpretation this infinite sum, for a given $t$ , is that it will mostly sum zeroes and just "add" one single $s(t)$ of the aperiodic function $s(t)$ and thus just produce the value at $s(t)$... this sounds useless so i guess that i must not be interpreting ot correctly...
(in other words: so why not write $s_P(t) = s(t)$ and that's it...? Since i guess that $s$ being aperiodic, then $s(t+nP) = 0$ for $n>0$? Because $s$ without the subscript P is aperiodic i.e. non periodic!)
Or am I interpreting it wrong (i guess i do but why the hell don't they explain it clearly?!) I would rather imagine that it would be something like this infinite sum "placing" the value of $s(t)$ at integer multiples of the period $P$ (a bit like the dirac that fires when its arg is ==0)? But if it is so please can someone indicate how this can ne inferred from the formula... since $s$ is aperiodic (and only $s_P$ is periodic)? Or of course explain how one should interpret this so-called "periodic summation "?
ok i really think i do get it now: as said in comments it is linked to the modulo, then i think the n that makes the expression s(t+nP) have a nonzero value for any t is in fact the result of the Euclidean division of t by P and hence t-nP is the same as t mod P ... i will do a numerical example to convince myself: let P be 8 and t be 10 then we have 10//8 = 1 remains 2 so thr argument of s is then 10-1*8=2 . Correct? with // meaning Euclidean
i dont see why i understood this same sort of formula for dirac summation and not this but well..