Methods of scaling FFT power
In displaying the PSD of signals it's common practice the subtract the DC component first;
$$ x_{ac} = x_{tot} - x_{dc} $$

So that spectral leakage will not suppress low magnitude high frequency components.

Furthermore, in some spectral analysis applications one may need a proper scaling between what is computed by the DFT of the windowed sampled sequence $v[n] = w[n]x_d[n]$ and the true continuous time CTFT spectrum $X(\Omega)$ of the analog signal $x_a(t)$.

That scale will be a function of the window length $M$ and sampling frequency $F_s$. Lets see the implications of this from an example:

Consider a continuous-time signal $x_a(t) =  \left( \frac{\sin(W t)}{\pi t} \right)^2$ whose CTFT $X_a(\Omega)$ is 
$$ X_a(\Omega) = 
\begin{cases}   
A (1 + \frac{\Omega}{2W}) &amp;, \text{for} -2W &lt; \Omega &lt; 0 \\
A (1 - \frac{\Omega}{2W}) &amp;, \text{for} -0 &lt; \Omega &lt; 2W \\
\end{cases}
$$

Which is a bandlimited triangular pulse with $A = X_a(0) = \frac{W}{\pi} $ These two signals are plotted below from their formulas for $W = 7\pi$ rad/second.



Now, this analog signal is (critically) sampled with a sampling period of $T_s = \frac{2\pi}{4 W} =\frac{\pi}{2W} $ such that we obtain the sampled discrete-time signal $x_d[n] = x_a(nT_s)$ as
$$ x_d[n] =  \left( \frac{\sin(W n T_s)}{\pi nTs} \right)^2 = \left( F_s \frac{\sin(w_c n)}{\pi n} \right)^2 $$

Where $w_c = W T_s $ and $F_s = 1/T_s$. In particular for the selected critical sampling rate $w_c = W \frac{\pi}{2W} = \frac{\pi}{2}$ and $F_s = \frac{2W}{\pi}$.  At this stage we can consider the DTFT $X_d(e^{jw})$ of the sampled sequence $x_d[n]$ either from its formula as given above or from the relation between $X_d(e^{jw})$ and $X_a(\Omega)$ from the sampling operation as given by:
$$ X_d(e^{jw}) = \frac{1}{Ts} \sum_k X_a( \frac{w-2\pi k}{T_s}) $$

It can be seen (by either methods) that $X_d(e^{j0}) = \frac{1}{T_s} X_a(0) = \frac{W}{\pi T_s}$. With $T_s = \frac{\pi}{2W}$ it becomes $X_d(e^{j0}) = \frac{1}{T_s} X_a(0) = 2(\frac{W}{\pi})^2$ which is $98$ for $W=7 \pi$.

Plotting $x_d[n]$ and $X_d(e^{jw})$ yields the following:


It can be seen that the discrete-time frequecy spectrum is extending from $w=-\pi$ to $w=\pi$ as it was critically sampled.

Now we shall return to obtaning a finite-length set of samples $v[n]$ from $x_d[n]$ by a sutiable window of length $M$ :
$$ v[n] = w[n] x_d[n] $$ 

From which the DTFT $V(e^{jw})$ is deduced as
$$V(e^{jw}) = \frac{1}{2\pi} V(e^{jw}) \star X_d(e^{jw}) = \frac{1}{2\pi} \int_{-\pi}^{\pi} W(e^{j\theta}) W(e^{w-j\theta}) d\theta$$

At this point we have to specify a particular window type such as rectangular, Hamming or Kaiser etc. Lets choose the simplest such as rectengular window of length $M$ whose DTFT is:
$$W(e^{jw}) = e^{j w \frac{M-1}{2}} \frac{ \sin( w M/2) }{ \sin(w/2) }$$
Note that the peak value of $|W(e^{jw})|$ is $M$ 

Lets evaluate the result of this convolution at the frequency $w=0$:

$$V(e^{j0}) = \frac{1}{2\pi} \int_{-\pi}^{\pi} W(e^{j\theta}) W(e^{-j\theta}) d\theta$$

The exact integration is difficult. But proivded that the window length $M$ is long enough so that the spectrum of the window $W(e^{jw})$ is highly concentrated in its main lobe which is between $-\frac{2\pi}{M} &lt; w &lt; \frac{2\pi}{M}$ and has a width of $\Delta_{ML} = \frac{4\pi}{M}$ , we can get an approximation for $V(e^{j0})$ as

$$ V(e^{j0}) \approx 0.5 \frac{1}{2\pi} X_d(e^{j0}) W(e^{j0}) \frac{4\pi}{M} = X_d(e^{j0})$$The approximation gets better as $M$ gets larger.

Hence we conclude that the scaling for the DTFT $V(e^{jw})$ is the same as that of $X_d(e^{jw})$ for a rectangular window of long enough length $M$ (the scale may be modified with the sum of window length for other windows lengths)

Finally we shall consider the DFT $V[k]$ associated with the DTFT $V(e^{jw})$.
Since for finite length signals (such as $v[n] = w[n]x_d[n]$ of length $M$) the DFT values $V[k]$ are uniform samples of the associated DTFT $V(e^{jw})$ there is no further scaling due to DFT stage. We conclude that:

$$\boxed{ V[0] = V(e^{j0}) = X_d(e^{j0}) = \frac{1}{T_s} X_a(0) = \frac{W}{\pi T_s} }$$