suppose I know the frequency response of a (linear) model approximating a real physical system but only at a specific frequency $f_0$ (so basically I have a complex number whose module is the magnitude response and the phase is the phase response).
In Matlab I want to filter a sinusoidal signal whose frequency is $f_0$ by a filter that approximates the response of my system at $f_0$ without altering the other frequencies. The filtering process must be done simulating the on-line behaviour, assuming that the next samples of the signal are unknown.
In other words my question is this: how can I build a filter whose behaviour at $f_0$ is the same of my system and does not modify the other frequency components?
The motivation I am asking this is that I need to perform some transformations on the frequency response at $f_0$ of the real system exploiting the results of the Singular Value Decomposition performed on the frequency response at $f_0$ of the identified (linear MIMO) model that approximates the real system.
Thanks in advance