Spectral estimation in Spectrum analyzer
The methods you're mentioning are methods for estimating spectra from a (typically discrete) time-domain signal – what the &quot;classical&quot; spectrum analyzer (SA) does is not that!
The classical sweeping SA consists of four parts:

A tuneable oscillator
a mixer
a good filter
a power detector

Here, 1. and 2. are used to mix down different parts of the spectrum - either by sweeping (typical for completely analog SA) or stepping through a set of frequencies.
The output of the sweeping mixer is then filtered by 3., which effectively means 1.-3. are a method of getting a varying piece of RF passband down to a frequency where 4. can be used to measure how much power is in that piece of RF spectrum.
You'd use the instantaneous frequency of the oscillator as x-coordinate, and the power &quot;seen&quot; by the power detector as y-coordinate. That's your point!
Note how you're not looking at the whole spectrum at once. You'll find &quot;probability of intercept&quot; considerations in literature, i.e. how likely is it that a bursty signal is actually active when the SA &quot;tunes by&quot; and observes the frequency they're on.
There's nothing here that really deals with the time-domain signal. For all that matters, the signal simply &quot;has&quot; some energy at some frequency. No need to estimate the spectrum from some time signal – they're actually measuring the energy at a single frequency, then move on to the next.
If you want to know more, there's really many introductions to using a SA, and you'll find the same components (oscillator, mixer, filter, power detector) again, and how you can configure them (sweep speed/dwell time, amplification, filter bandwidths, sensitivities).
Now, I didn't use &quot;classical&quot; with quotation marks without reason: For the last ~20 years, SA typically do have the possibility to sample the mixed-down signal and analyze it to improve the resolution, to implement better filters, or to do signal analysis beyond estimating a spectrum. Typically, these measurement methods are pretty limited, even in upper-class SA; they are literally labeled &quot;FFT&quot; without specifying exactly what they do, but you can expect things to be Bartlett's method for as long as the SA dwells on one frequency. How the SA pieces together different spectral estimates from different tuning frequencies is something that I haven't even found in manuals. Armed with an SDR and time you can figure that one out, but in all honesty, that's rarely what you really need an SA for: SDRs and even oscilloscopes can give you a better spectral estimates (though I can tell you, as DSP guy, the nomenclature of some oscilloscope vendors describing their spectral estimation methods drives me nuts).