Relation between Power Spectral Density and RMS of the signal
instantaneous power is:

$$ p_x(t) = |x(t)|^2 $$

mean power is:

$$\begin{align}
 P_x &amp;= \lim_{T \to \infty} \quad \frac{1}{T} \int\limits_{-\frac{T}{2}}^{+\frac{T}{2}} p_x(t) \, dt \\
\\
&amp;= \lim_{T \to \infty} \quad \frac{1}{T} \int\limits_{-\frac{T}{2}}^{+\frac{T}{2}} |x(t)|^2 \, dt \\
\end{align}$$

the relation between Power Spectral Density to mean power is:

$$ P_x = \int\limits_{-\infty}^{\infty} S_x(f) \, df  $$

the relation between Root Mean Square to mean power is:

$$ P_x = \lVert x(t) \rVert^2 $$