Suppose I have two signals $f,g$ which are orthogonal in the sense of the usual inner product on $\mathbb R^d$. Then if I'm not mistaken these signals have disjoint spectral support, i.e their fourier transforms have disjoint support. Suppose further that I know the spectral supports aswell. How can I make use of this information in order to sample only one of the signals, i.e, sample so I don't "see" the other at all?
The trivial solution seems involve filtering out the irrelevant frequencies using an ideal filter, but that's not an option; I am restricted to "physical" solutions.
It's fine to assume $f,g$ are well-behaved.