Various things seem to be getting mixed together here so will try to work through it all and see if I can clear up a few things.
Ok, most important thing first - sound is analogue. (It's inherent. Sound is a pressure wave and a consideration of the fundamental forces at play will show why it's analogue.)
If you look at the waveform of sound it will therefore be an analogue waveform.
Also important to note here that the images in your post aren't of the waveform of the sounds. They're of spectrograms of the sounds.
Sound will usually be composed of many different frequencies simultaneously. Roughly a spectrogram shows the relative strength of the different frequencies.
Just gave the acoustic part of the Canonn website a read regarding the Brains:
https://canonn.science/codex/brain-tree-phenomenology-part-2-analysis-of-acoustic-features/
Something occurred to me, though. I did a little reading about Digital audio and Analogue audio:
http://www.explainthatstuff.com/analog-and-digital.html
A simplified video:
https://www.youtube.com/watch?v=XCu6L4kQF3k
To me, this picture looks like the Brain Trees are Analogue - basically, the sounds need clearing up to make it come out clearer because the Hz or Khz are out of whack (beyond me, though):
https://i.imgur.com/e88WWgj.jpg
Braintrees are organic. A digital signal coming from an organic would be extremely surprising. So whatever it is from the Braintrees that's generating the sound would result in an analogue signal. This is exactly what would be expected.
The signal being analogue doesn't mean that it needs cleaning up though. That's not what analogue means. I can see how the video might have lead to that impression, but that's not what it means.
I'm not sure what you mean by the Hz or KHz being out of whack, so just to clarify in case you've not really dealt with this stuff before and the meanings weren't clear: Hz (Hertz) is a measure of frequency. 1 Hz is 1 cycle per second (Units are 1/s). A kHz (kiloHertz) is just a short way of writing 1,000 Hz. Whether you write a frequency it in Hz or kHz (or mHz, MHz, and so on), the actual frequency is the same.
Also, again it's important to bear in mind that the images are spectrograms, not the waveform.
The Ancient Ruins are Digital:
Well... Yes and no. Mainly no though. On the whole they're not.
The 'yes' part first - the obelisks are digital. Well they are if Ram Tah is to be believed anyway. He says the Guardian computers are based on the same principles as ours, and our computers are digital.
The 'no' part...
Firstly, the main thing we're talking about here is the sound, so it's analogue, not digital.
Secondly, the 'barcodes' are specifically from the obelisks and they're only part of the ruins. The 'barcodes' don't appear in the sound from other bits of the ruins, and the other parts of the ruins don't appear to be computerised and so aren't digital in that sense either.
Thirdly, again it's the spectrogram that's being looked at, not the waveform. What's being seen is something that's being built into the noise so that it appears in the spectrogram. It's exactly the same principle as the images that are hidden in the audio from the Unknown Probes and Unknown Device (and that picture of David Braben that was hidden in a spectrogram!).
Fourthly, the 'barcodes' in the obelisk audio spectrogram are not images of a digital signal. They're built from 5 components. It's not a single thing that's on or off.
An important point about this image - the 4 individual images that this is composed of have been either widened or compressed so that they are all the same width. This is distorting things. See the last block on the right in each of the rows? They should all be the same size. And across all the other blocks there should only be a total of 4 shapes.
Could this really be the difference in sounds?
They aren't barcodes, but merely need the sound re-adjusting to clear/clean them up?
'Barcodes' is only a nickname for the images in the obelisk audio spectrogram, so not really sure what you mean by this tbh. Is what the difference in the sounds?
Also I haven't mentioned it yet but you can't hear the 'barcodes' in the obelisk audio - the frequencies are beyond our hearing range. You need to do a bit of manipulation of the audio to make them hearable (Cut everything below 10kHz, lower pitch substantially, cut out noise and boost volume), which I've already done, here:
...snip... Anyway, on a slightly different topic I've converted one of the passages to audible frequencies just to see what it sounds like (by a passage I mean one group of blocks with the end of the group denoted by the thick full height block.):
https://clyp.it/kos3vra0?token=83535143a90b2ce3dea353b966b49190
The scratchiness of the sound is probably down to the editing - there was quite a lot of noise reduction and other editing to get it audible.
I'm not quite sure what to make of your last point. Which sounds is it that you think might need cleaning up? (Hopefully I've covered the Digital/Analogue side of things already.)
If there is no way to do that, then this probably just serves to show us that one uses Digital and the other Analogue - could also explain why the Brain Trees are on worlds that have volcanism so that the signals are protected by a magnetic field (or to just protect the trees themselves from radiation)?
