Equalizing a digital signal, involving Matlab

[Inertigratus]

Homework Statement

A signal goes through a black box and out comes another signal.
Now I have the signal that came out and need to find the signal that went into the black box.
This by analyzing a test signal and the output of that test signal.
The analysis is done in the frequency domain. The test signal is using one specific frequency.
The signals are sampled using a specific frequency (different from the test signal frequency).

Homework Equations

Y(ω) = H(ω)X(ω)

The Attempt at a Solution

I know how the output depends on the input, but decided not to write it here since it's not necessary for my questions.
So I can find H(ω) by doing the division Y(ω)/X(ω) using the test input and output.
However this only gives me H(ω₀) where ω₀ is corresponding to the specific frequency used only for the test signal.
Using additional information (that I haven't provided here) I can find constants that make up the frequency function H(ω) for all frequencies.
However, the constants are multiplied (to make H(ω)) by an exponential powered to iβω.
Now what I'm wondering is, what frequency should I use, what "ω" should the exponential be powered to?
The sampling frequency?
Maybe what I'm asking is, which frequency is the "real" output using? the one for which I'm trying to find the input.
To clarify, H(ω) looks something like this: A₀ + A₁e^-2πfβ. Which is for all frequencies, but I'm working numerically in Matlab and am not sure which frequency "f" is.
Isn't it simply the sampling frequency for the signal?
It's probably difficult for you people to get into this problem without having worked with it, hope I made some sense atleast.

 

[Inertigratus]

Perhaps someone could take a look in Matlab?
I could send the code/files, it's not that much.
My code is pretty much finished, it's just that there's some (probably minor) mistake that I can't figure out.
Would be greatly appreciated!