There are different methods here too. In this case I'll show you the unfiltered and poorly filtered results because I don't have high quality Gaussian or sinc filters implemented for this purpose. I also don't have a CRT (tube+beam+phosphor) emulator, although if I recall correctly mystran provides one on his site that works reasonably well.
As you can see the peak level of the waveform is varied because the peak level of the sampled signal is varied. In order to measure the actual peak level a complex sinc filter is required.
Alternatively using a Gaussian filter it is possible to reduce HF content to zero and more accurately measure peak level but this is typically not what you want in these cases.
To better demonstrate this effect I'll zoom the waveform from a higher frequency so I can apply cheap filters so you can see the change:
Unfiltered.
Cubic kernel.
As you can see in the second image the peak level of the waveform is more accurately approximated, although the filter isn't steep enough to produce a perfect result there are less "valleys" in the waveform.
A CRT model overcomes this issue by not filtering the signal at all... although in such cases the intensity of the result is highly variable due to interference patterns and often times 8-bit color is not nearly enough. (Need floating point to accurately produce good results.)
... unfortunately now I can't figure out where that CRT modelling plug-in I thought existed was...
