# Is Spectral Coherence (MSC) dependent to the initial amplitude of the comparing signals?

Given the signals

\begin{align} x(t) &= A_1\sin(\omega t)\\ y(t) &= A_2\sin(\omega t) \end{align}

Do $A_1$ and $A_2$ play a role in the $C_{xy}$ coherence estimator? MATLAB's mscohere.m shows no differences for $A_1=A_2$ and $A_1\neq A_2$ at all.

$$C_{xy}(f)=\frac{|G_{xy}(f)|^2}{G_{xx}(f)G_{yy}(f)}$$
with the cross-spectral density $G_{xy}(f)$, and the power spectra $G_{xx}(f)$ and $G_{yy}(f)$, respectively, it is clear that scaling of $x(t)$ or $y(t)$ does not change the value of $C_{xy}(f)$, because the scaling constants appear in the numerator as well as in the denominator and cancel out.
The coherence is a normalized quantity (and hence scaling-invariant), and it always satisfies $0\le C_{xy}(f)\le 1$.