measuring how much signal corrupted by passing from a medium I am looking for a measure to report how much a signal has corrupted by passing a medium.

Suppose we have a signal 2Hz and amplitude 1. I pass it from a medium. A receiver got the signal with 2Hz, amplitude 0.5 and a few more signals.
Convolution gives me an array that say with a specific delay overlapping between input and output is maximum. 
Do we have a measure to report a single scalar how much a signal has corrupted?
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.