First of all, please forgive me for not providing any context, as I cannot.
I wondered: Suppose there are two functions $a(x)$ and $b(x)$, each contains a few discrete frequencies.
So, their Fourier transform $A(x)$ and $B(x)$ are just some spikes.
The two functions may have some common frequencies $f_1, f_2,...,f_k$.
Then, is there a certain mathematical way(maybe a transform) to produce a new $a(x)$, $a’(x)$, such that any non-common frequencies are removed from $a(x)$, while the common frequencies remain present with amplitude unchanged?
In short, is there a way to mathematically preserve only the resonance part?