Here is a sound example for what follows.
Let's assume we have a signal
$$s(t) = r(t) + e(t)$$
$r(t)$ is a signal which is recurrent with a given period, i.e. in my example $r(t) = $ the exact same snare sample, which is played every 1 second, starting at 00:00:00,500
$e(t)$ is an evolving sound (in my example it's the synth pad soft sound)
I assume the signal is mono, and that no compression or other master effect has been applied.
How to recover $r(t)$ from the mix $s(t)$, by analyzing which "pattern" is recurrent in $s(t)$? (the period 1 second is considered as given)
In one word, how to isolate the snare sound from the mix?
I would like to do it by slicing the signal each 1 second:
and analyze what part of signal is recurrent (= the snare) and which is not (= the synth) among all slices ?
Is there a separation algorithm based on analyzing recurrent parts / non-recurrent parts? Using FFT or something else?