Topic: Kill the self-noise!?

[TheJez]

Hi all,
I'm not sure if this is the right sub-forum to discuss this. If not, please let me know.
Anyway: With all the discussions about single and multi ADC 32bfp systems, something popped up in my mind... It's not something to improve the dynamic range but to reduce the self-noise... I'd like to know if I'm onto something or if this idea's complete nonsense...
The idea is quite simple: The input of a recorder is being fed to two identical paths A and B, consisting of some analog electronics (amplification) and the A/D converter (which also has some analog and digital stuff inside). Next, each sample pair coming out of the ADC's is summed and then divided by two. See attached image.
So why would you want to do this? Well, the idea is that the analog signal going through the AD converter is determined by the signal coming from the microphone (or whatever other input) plus some random additional self-noise created in the analog path. The key is in the randomness of the self-noise. Adding two random noise signals with a certain average amplitude creates another random noise with the same average amplitude. (This is where I may be wrong...) So the dividing by two effectively reduces the self-noise by half (-6dB) while the signal level remains the same! Doing the same trick with four identical paths would reduce the self-noise by -12dB etc...
I have no idea about costs of components in recorders, but I can imagine a recorder can get quite expensive when it is optimized for low self-noise using a single path. Maybe, using this trick, it is cheaper for manufacturers to create low-noise recorders by combining output of two or four cheap & noisy audio paths instead of creating a single low-noise audio path...
Where am I going wrong with this idea? There are some very smart people on this forum who may have some thoughts about this...

[datbrad]

You just described what sounds to me like Dolby/DBX analog noise reduction combinded with Dither.

[Gutbucket]

Makes sense.  As far as I know what you describe is a strategy currently used inside AD/DA converters which predates the switching ADC tech.  The converter chip may support something like 8 channels, but if only two are needed then half of them can be run in parallel to improve performance. Doing that incrementally reduces noise in the way you mention, and lowering the noise floor increases dynamic range by that same incremental amount.  Compared to the more switching that needs to be done between channels running at different levels, this just requires simple summing, but the performance increase is not as large.

I think you end up getting 3dB of improvement per doubling of paralleled channels, so four parallel paths improves things by 6dB.  ..because summing two channels of random noise at the same level increases the level of noise in the summed output by 3dB, while summing two correlated signals at the same level increases the summed output by 6dB. But someone please correct me on that if I'm wrong on that.

I think that electrical summing works in the same way as what is happening acoustically when boundary-mounting a microphone, where I am sure of what happens.  In that case the boundary layer causes a 6 dB increase in gain for direct arriving sound but only a 3 dB increase in gain for diffuse/reverberant arriving sound, increasing the direct/reverberant ratio by 3dB.  The parallel analogy between electrical verses acoustic signal summation of uncorrelated noise and correlated signal is interesting.

Pretty sure Eberhard Sengpiel included the correct calculation for it somewhere here:
https://sengpielaudio.com/Calculations03.htm

[edit- Not really related to Dolby/DBX noise reduction, which are compander based schemes that squeeze a bit of additional range through a single channel]

[kuba e]

Thank you TheJez for a very nice topic. I also think that the rule for the sum of direct/diffusion sound is the same for the electrical signal/noise. I remember the discussion about the boundary mics very well. I asked why there is difference  in increase 3 db for the direct and diffuse sound. It is explained here:
https://taperssection.com/index.php?topic=186619.0

And a very nice explanation is also in this thread:
https://physics.stackexchange.com/questions/389058/why-do-two-coherent-sounds-add-up-6db

[morst]

The key is in the randomness of the self-noise. Adding two random noise signals with a certain average amplitude creates another random noise with the same average amplitude. (This is where I may be wrong...) So the dividing by two effectively reduces the self-noise by half (-6dB) while the signal level remains the same! Doing the same trick with four identical paths would reduce the self-noise by -12dB etc...

To the extent that the random noise is randomly correlated, won't the correlated bits have a higher amplitude of noise by +3dB?


But totally uncorrelated sounds will ... decrease the level of noise?
Or just make a different kind of noise?


Great food for thought. Be cool if it works!
Massively parallel tracking for noise reduction!?
If each doubling of track count reduces noise by -3dB then how many doublings are required to get to the desired noise floor?

[TheJez]

Thanks all for your reactions! It's nice to see I was not totally crazy when this idea popped into my head, although I had the math wrong. (I already somehow felt it couldn't be that easy...) It did prove once again that my knowledge on acoustics and analog electronics is not on the same level as some of you smart people on this forum! I really enjoyed reading about the boundary mic stuff! I think I've used it once completely by accident where circumstances kind of made me mount my mics like that, and to my surprise it resulted in one of my finest sounding recordings.
If the multi-path technique would be used, I wonder how much of the self-noise would be uncorrelated. I can imagine that at least some of the noise would be introduced by power supply noise hence possibly common for all paths. (Unless each path will get its own power supply electronics or even their own batteries!) And then again, would it be useful at all to get EIN down to -150dB or something, other than for marketing reasons?...

[Gutbucket]

Yeah, when summed the noise from from two different fully uncorrelated sources (from different ADCs, different mic capsules, multiple arrivals of diffuse reverberant sound in a boundary mounted mic) increases in level by +3db, while fully correlated signals (shared identical content, direct arriving sound) increases by +6dB, for a net improvement of +3dB.  If not fully correlated/decorrelated the net difference will be less than 3dB.  Would seem the practical limitation is that the reduction in noise is linear (-3dB, -6dB, -9dB) while the device count increases geometrically (2, 4, 8, 16..), but I imagine there is a real-world limit of how far you can practically take it.. probably follows an asymptotic curve.

I've seen some DIY mic builds that use multiple omni capsules tightly grouped together and summed to improve noise performance over that of a single one, performing essentially like a single diaphragm of the same diameter..  Not sure how well it works or if such an arrangement introduces more problems than it solves or not.

Taking it several steps further.. combination of multiple non-coincident sensors arranged in a specific array, along with the output being summed in more complex ways that includes phase and level manipulation is the basis of "beamforming" in radar, sonar, and optics.