measuring how much signal corrupted by passing from a medium
The most typical measure of a signal corruption (or degradation) would be an error squarred integral (or sum for discrete case), preferably normalized such as:

$$ \epsilon = \frac {\int (x(t)-x_r(t))^2 dt}{\int (x(t))^2 dt} $$

Where $x_r(t)$ is identified as the received and corrupted signal. The interval of integration choosen to fit into signal duration of interest.

This is an unweighted (or equiweighted) calculation. If you think that certain features of the error is more impotrant, more relevant, more effective than the others, then you could reflect this by modifications such as simple linear weighting or onlinear processing of the error accordingly, which would produce more meaningful results.