Topic: 32Bit Float recording - The Technical view

[Ozpeter]

Without checking back all the pages of this thread, I may be repeating something already posted, but in the course of investigating something or other, I just came across this research document where a 32 bit float audio interface was tested in remarkable depth.  It might be of general interest to those in this thread.  Or incredibly boring...

https://www.researchgate.net/publication/374782111_An_experimental_investigation_of_32-bit_float_ADC_systems_-Zoom_UAC-232_Test_Report_using_Multi-Instrument

[Gutbucket]

Thanks Peter. Saw that back when and re-read it again over the weekend.  The tests confirm Zoom's switching ADC architecture achieves the goal of extending dynamic range in a way which seems to be fully sufficient for our concert recording needs.  And it somewhat explains how the same may not be true for some esoteric sound design uses due to the level of its noise floor modulating along with the ADC switching, which does not cause any problem for concert recording where the noise floor is fully masked by either the music itself or by other sources of noise in the signal chain at the levels around which the switching occurs.  Presumably the results carry over to the Zoom recorders using the same or similar tech as the interface.  Would love to see such an analysis done on the recorders TS members are using.

What isn't confidence inspiring is the parroting in the introduction of a marketing-driven untruth we've discussed previously, made without any backing attribution (as usual).  That's unfortunately become par for the course in marketing materials but is inexcusable in a supposedly rigorous technical paper reporting test results.  Would love to know if peer-reviewers of the paper (if any) called it out.  This establishing statement made in the introductory paragraph struck me as admirably clear and precise: "Ideally, the noise level would only cause the least significant bit to toggle while the maximum level would fully utilize all bits."  Reading that I thought, "Yes! That is the goal, clearly and concisely stated." [smiles] ..and based the limits of the device as explored in these tests, that easily fits within 24 bits" [raised eyebrow].  Only to be immediately let down upon reaching the second paragraph by the claim stating- "Audio that is too loud will be clipped at the top of their waveforms while audio that is too quiet will lack fidelity or even be buried in the noise floor (see figure below).'' (< bolding for emphasis is mine)  Clipped, yes.  Buried in noise-floor yes.  Lacking fidelity no.  In making that claim, the onus is on the author to explain why digital sampling theorem suddenly no longer applies.

Making it more egregious is the inclusion of the misleading marketing illustration that follows, showing a stair-step output response at "weak signal" levels.   Whenever you see that you should immediately be wary, because in making that claim (seemingly always without attribution) the author has almost always sabotaged their own credibility.

Scale up the analog output from any digital recording which was properly frequency limited to fit within the passband imposed by the sampling-rate (achieved via proper design of the ADC), and which, in the author's own words, "Ideally, the noise level would only cause the least significant bit to toggle.." and and show me stair steps.  There are none.  The presence of noise sufficient to cause the LSB to toggle randomly eliminates low-level quantization error.  Injecting dither noise if needed to achieve that has long been correct practice for an old problem solved long ago.  The presence of additional noise further removes all possibility low-level quantization error occuring. 

Otherwise, great to see these kinds of in depth test results and, ignoring that difficult to overlook bit of bs in the introduction, the testing seems good to me.  Experts are welcome to correct me if I'm missing something in those results which might prove problematic for concert recording. 

More on why the stairstep drawings are misleading and claims of "lack of fidelity" are bs here (great video made 12 years ago, link to which has been posted a number of times around TS)-
https://youtu.be/cIQ9IXSUzuM?si=-YpzlQRgKEOQIOIe&t=216

Reaction / further-explanation to the above above (posted a 2 years ago, the truth is unchanged)-
https://youtu.be/cD7YFUYLpDc?si=aMevn5fMs8keOkmq

[Ozpeter]

^  All good thought provoking stuff! 

This morning I had a new thought.  For once. 

Companies making single ADC devices writing 32 bit float data from the 24 bit output of the ADC could be adding a multiplier to the data to make it look like real 32 bit float.  Say the multiplier was 1.2 - so what would have been written as 0.99 became 1.188 - and if 1.0 equated to full scale, the audio would look digitally clipped when editing.  But then of course you could reduce the level by a factor of 1.2 (or more) and the clipping would be gone.  And the user would think, wow, real 32 bit float helping to avoid clipping.  But actually it would be a con.  Hmmm.  I wonder if that is happening?

Note that my example has been expressed very crudely - I hope my point is clear.

[morst]

The multiplier is always a power of 2, so you would never see a multiplier of 1.2.

https://en.wikipedia.org/wiki/Single-precision_floating-point_format

an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2⁻²³) × 2¹²⁷ ≈ 3.4028235 × 10³⁸. All integers with seven or fewer decimal digits, and any 2ⁿ for a whole number −149 ≤ n ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value.

[Ozpeter]

The multiplier is always a power of 2, so you would never see a multiplier of 1.2.

https://en.wikipedia.org/wiki/Single-precision_floating-point_format

an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2⁻²³) × 2¹²⁷ ≈ 3.4028235 × 10³⁸. All integers with seven or fewer decimal digits, and any 2ⁿ for a whole number −149 ≤ n ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value.

Confession - that's over my head!  But maybe that doesn't change what I am saying.  In a DAW you can raise the gain of a normalized undistorted 32 bit float file, so that it now peaks above the maximum, and on replay it sounds clipped.  And of course you can later reduce that gain back to where it was and it is no longer clipped on replay.  What if the last process in the single ADC on the recording device increases the signal level unnecessarily as it outputs to the 32 bit float file, in just the same way as you can boost it in a DAW, so that when you open the file in your DAW it looks and sounds clipped, but you can normalise it back to an unclipped file, and think that the 32 bit float format has done something useful?   

I've just being doing some very simple tests with a single ADC 32 bit float recorder, recording from its internal mics.  Zoom claim that the device can record the maximum specified SPL level of the mic without clipping.  When I record a test tone from a loudspeaker at a neighbour-annoying level with the device held right up to the speaker, and open it on my DAW, it's over the top and clipped.  When I normalise it, the waveform is perfect (zoomed in to sample level) and it sounds fine.  But why is the audio being written to file above full scale when it doesn't need to be, as the max SPL of the mic wasn't reached?  Surely they could configure the device so that when the mic hits its maximum SPL, the 32 bit float file just reaches full scale?  As it is, a user might think that without 32 bit float, the audio would be unrecoverable, whereas if they didn't bump up the digits as they are written, there would be no problem? 

Maybe what you are saying is that 32 bit float is bumped up by a factor of 2 as part of the standard, not as part of a con by manufacturers. 

Anyway, I am actually impressed that the cheap single ADC recorder I tested (Zoom H2 essential) can actually record a very loud test tone without distortion - after normalising.  Even if the manufacturer is playing tricks.  Or not.

[morst]

I don't think IEEE is trying to mess with you, it's just that the multiplier bits in 32-float give a very wide dynamic range because it's powers of 2.
note that the bold in my quotes is my emphasis in my post above.
32-bit, base two means it's 32 on/off bits aka binary, aka base-2

https://en.wikipedia.org/wiki/Institute_of_Electrical_and_Electronics_Engineers


Seems like you have not reached the limits of the loudness your mics can handle yet, but making over-level-looking WAVs is sufficient for this demo.

[TheJez]

The multiplier is always a power of 2, so you would never see a multiplier of 1.2.

https://en.wikipedia.org/wiki/Single-precision_floating-point_format

an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2⁻²³) × 2¹²⁷ ≈ 3.4028235 × 10³⁸. All integers with seven or fewer decimal digits, and any 2ⁿ for a whole number −149 ≤ n ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value.

I think the important word in the quote about IEEE 754 32bfp is 'exactly'. It means we may no be able to multiply the samples by exactly 1.20000000000, but instead it will be multiplied with 1.199999998796 or whatever. I also guess you may be misinterpreting the 8-bits exponent inside the 32 bits, which is used to multiply the lower 23 bits with 2^exp. This is just a way to store a floating point value, and has nothing to do with the ability to multiply two whatever floating point values. So we can multiply samples with a value (very close to) 1.2.
What floating point format would it be if a value cannot be multiplied by (something very close to) whatever other floating point value.

[TheJez]

I've just being doing some very simple tests with a single ADC 32 bit float recorder, recording from its internal mics.  Zoom claim that the device can record the maximum specified SPL level of the mic without clipping.  When I record a test tone from a loudspeaker at a neighbour-annoying level with the device held right up to the speaker, and open it on my DAW, it's over the top and clipped. 

Typically 32bfp devices have some form of digital gain control. Basically this is just some logic that simply multiplies the output of the single or dual ADC samples. This is done in the 32-bit realm, so it won't introduce clipping when the multiplied value goes over 0dbFS. On the F3, this is the 'wave magnifier' (1x, 2x, 4x, 8x etc) or whatever it is called. On my Tascam FR-AV2, it is a slider than can be set from 0dB to +40dB or something. I don't own a Zoom H2 Essential, so I just scanned its manual and it seems there is indeed no way to control the digital gain on this device. As you can get levels > 0dBFS when recording, it seems Zoom indeed picked a fixed digital gain > 1x . Is it bad intention to justify the 32bfp format? I guess we will never know, but personally I doubt that. I guess they just picked a value that gives reasonable output levels on what they deem 'normal usage'.

@Ozpeter: Reading the manual a bit further, I do notice that it is possible to export the files to 32bfp, without normalization, yet with using the 'mixer settings'. In the mixer, you can set the digital gain from -80dB to +40dB. Could it be you used that way to get your files into your DAW, unintentionally applying a digital gain > 0dB?

[Ozpeter]

No, although I did experiment a bit with that feature this afternoon.  You have to go through some hoops to process the already recorded files, and I did check the 'mixer' when recording wasn't doing anything (set to zero).  I do admit that if the device was configured so that the loudest audio without mic or preamp clipping was full scale in the 32 bit float file, then quieter stuff would be rather quiet for immediate listening.  Maybe that's why they digitally amplify it, as you imply.

Not directly on the immediate topic, but related, I did a little test where I recorded the loud tone from the speakers, close to analog clipping (which the H2e warns you about on its display), and also recorded some 'silence' in a quiet room under a rolled up duvet.  The result seemed to me quite good when analysed.  When the combined files were normalised, the 440Hz tone peaked at zero of course, and at that frequency the subsequently recorded silence was at about -100dB on a frequency analysis display.  At 10kHz, the 'silence' was down to about -120dB, and slightly quieter at 20kHz.  The chances of anyone being disturbed by system noise with those figures would only be likely if the recording involved a small bird 100m away, in a very quiet country location, with a lot of gain added later.  Or so I think.

[Gutbucket]

I guess they just picked a value that gives reasonable output levels on what they deem 'normal usage'.

That's my presumption.

If a hot input signal clips the input buffer or the "high level" ADC, such clipping occurs in the analog realm prior to, or in the course of digitization, and is irreversible. 

If clipped via a digital increase in gain after digitization to 32bit-floating point, it's reversible.

Many are likely to confuse those two things and assume it's the 32bit float part of things that's responsible for avoiding the clipping while recording, when its actually the multiple-ADC switching scheme.. which will clip upon reaching it's realworld upper level input limit.

[TheJez]

Not directly on the immediate topic, but related, I did a little test where I recorded the loud tone from the speakers, close to analog clipping (which the H2e warns you about on its display), and also recorded some 'silence' in a quiet room under a rolled up duvet.  The result seemed to me quite good when analysed.  When the combined files were normalised...

Assuming they match their analog and digitals component well, then one would think the upper limit of the analog stage would be just below the upper limit of the ADC (which would then output just-below-0dBFS samples). As you recorded very close to the analog stage upper limit, the resulting 'loudness' of the recorded file (so without normalization) should give a reasonable estimation of the fixed digital amplification they apply. Do you remember how much gain reduction was applied when normalizing?

When the combined files were normalised, the 440Hz tone peaked at zero of course, and at that frequency the subsequently recorded silence was at about -100dB on a frequency analysis display.  At 10kHz, the 'silence' was down to about -120dB, and slightly quieter at 20kHz.  The chances of anyone being disturbed by system noise with those figures would only be likely if the recording involved a small bird 100m away, in a very quiet country location, with a lot of gain added later.  Or so I think.

Agree... Likely situations where one would attach a less sensitive mic (e.g. for high dynamic recordings or high SPL situations) would be more challenging. Having no analog gain control and just a single ADC would likely drop down the SNR.

[Ozpeter]

Unfortunately I am not at home for several days now, but I will respond to above question re levels as soon as I can.