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I have a signal recorded from two different detectors, with different levels of gain.

$$ S_{1}(\omega) = \alpha_{1}S(\omega) + \beta_{1} \\ S_{2}(\omega) = \alpha_{2}S(\omega) + \beta_{2} $$

How would you correct for the gain, considering the offset in the signal is minimial.

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    $\begingroup$ Are you sure that is a constant offset in frequency? That would correspond to $s_1(t) = \alpha_1 \cdot s(t) + \beta_1 \cdot \delta(t)$ in the time domain. $\endgroup$
    – Hilmar
    Feb 13 at 10:33
  • $\begingroup$ Now, that I think about it, I guess it would rather be $S_{1}(t) = S(t)\otimes \alpha_{1}(t)$, where $\alpha_{1}$ basically is the instrument response function. $\endgroup$
    – Fracton
    Feb 15 at 8:22
  • $\begingroup$ Are your gains, or instrument response functions, known? This is easy and obvious if they are, perhaps impossible without some side experiments or calibration if not. $\endgroup$
    – TimWescott
    Feb 17 at 17:16

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