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Can you hear under the noise floor? (digital audio)

tuga

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I found the following in an old white paper from Lavry Engineering titled "20 Bit Equipment For 16 Bit Work?".
It would be interesting to hear comments from the digital audio experts.

Can you hear under the noise floor?

The engineering definition of the "noise floor" is a measure of the total combined noise energy
residing at all frequencies simultaneously. While such a definition can serve well for comparing
signals or equipment, it may be rather misleading as an indicator for hearing capabilities. The ear
"does not listen" to the energy present at all frequencies simultaneously. The ear-brain combination
is a very competent tool for comparing the energy at a given frequency to the energy levels in the
surrounding frequencies. It can hear much lower signals then indicated by the total noise figure. The
frequency plots (FFT plots) provide a very good estimate of how far down you can hear a steady tone.
If you can see a tone above the noise floor, you will not hear it. In other words, the proper "yard stick"
is the noise floor density (energy at each frequency).

Undithered signals behave erratically. We have shown a case where an almost negligible signal is
"amplified" to become 1 LSB square wave. One may hear a -200 dB tone with a 16 bits undithered
system. One may choose to view the opposite case, when both the signal and noise are gated off,
as the hearing threshold of an 16 bit unditherd system (about -96dB). Both are "special cases" and
an undithered system can not provide a good standard for hearing sensitivities.

Dithered signals provide a "constant" noise floor, independent from signal and DC offset.
Measuring a triangular dither with a "dB meter" shows a reading of -93 dB for 16 bits. The energy
density (at each frequency) is at about -125 dB. Can you hear under the noise floor? You can hear
30dB below your "meter", all the way down to the noise density in the surrounding frequencies.
Reexamination of the frequency plots shows that you can hear a 16 bits dithered signal down to about
-125 dB under full scale.

Some manufacturers choose to view the special case of undithered signal gating as a the 16 bits
hearing threshold. One should not confuse the "gating threshold" of unditherd system with the noise
density of a dithered one. The "special gating case with 1/2 LSB of DC" occurs at about -96 dB. The
noise density (per frequency) for dithered signals is almost 30 dB lower.

The ability of the dither "to to bring the gated signal back" is shared by all types of dither.
Rectangular, Nyquist and triangular all perform the task within about 3 dB of each other (a range of
about 1/2 a bit). Beware of claims for "a special ability" of a specific type of dither to provide "3 -4
more bits". The 30 dB or so of dynamic range "beyond" the gating threshold is not unique to one type
of dither. It is shared by all types of dither and is not to be confused for additional bits. The proper
criteria for dither quality is its ability to eliminate distortions and noise modulation.

Noise shaping improves the noise floor:

The ears can hear music energy only while above the energy in surrounding frequencies. The
noise floor limitation (due to limited available bits) can be reduced by a noise shaper. The noise
shaper reshapes the frequency content of the quantization errors: it moves noise from hearing
sensitive regions (such as 2-4KHz) to less sensitive regions (such as 15-22KHz),. The process
trades off a better noise density floor where it counts for increased noise where it matters less. We
will not deal with how to choose from the a selection of available number of noise shaping "curves",
all based on psychoacoustic research under various condition.

The following discussion will use a noise shaper from a paper titled "Minimally Audible Noise
Shaping" by Stanley Lipshitz, John Vanderkooy and Robert A. Wannamaker (the leading experts in
the fields of dither and noise shaping). The plot below shows that the noise is "shaped" according to
some hearing sensitivities curve. The process includes dither and the shape of the noise is constant
and is not dependent on the signal or DC offsets.

The initial introduction of the modern concept of noise shaping encountered some resistance from
dither hardware manufacturers, confusing some users by comparing it to equalization and claiming
that it is unnecessary because most recording work yields no better then 90 dB outcome. Noise
shaping does not equalize the signal. The quantized signal is left untouched. Noise shaping
processes only the quantization errors (noise). As explained earlier, The "90 dB of dynamics"
argument is improper because it addresses the combined total energy across the audio frequency
band, while the real goal is to improve the noise density at each frequency.
 

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  • Lavry_20 Bit Equipment For 16 Bit Work.pdf
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Blumlein 88

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All true.

Also a paper from 1997.

Now I'd say who cares. We have 24 bit DACs, and linearity of the lower bits is a solved issue with sigma-delta ADCs and DACs. You still have noise limitations on the analog part of things. The best units can really do -120 db levels accurately. So nothing to see here really.
 
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tuga

tuga

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All true.

Also a paper from 1997.

Now I'd say who cares. We have 24 bit DACs, and linearity of the lower bits is a solved issue with sigma-delta ADCs and DACs. You still have noise limitations on the analog part of things. The best units can really do -120 db levels accurately. So nothing to see here really.

My question was more to do with the audibility (under the noise floor) side of things, hence posting in the Psychoacoustics sub-forum.
 

TheBatsEar

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One may hear a -200 dB tone with a 16 bits undithered system.
9f75259f7089ab3d7fa097c68be55e7fb27fbd135b079ea6310c7b2503ea22f6.png

Am i the only one?
 

MusicNBeer

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All true.

Also a paper from 1997.

Now I'd say who cares. We have 24 bit DACs, and linearity of the lower bits is a solved issue with sigma-delta ADCs and DACs. You still have noise limitations on the analog part of things. The best units can really do -120 db levels accurately. So nothing to see here really.
Yes, huge fat "who cares"! I can't even hear any noise when I do an unshaped dither to 16 bits. I don't even think I'd care if it was 12 bits.
 

TheBatsEar

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Why do they neglect to say how high you need to turn the volume control? and what happens to your speakers if a normal sound follows?
Someone post that McFly kid getting thrown around by that giant guitar amp speaker ... :D
 

earlevel

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I found the following in an old white paper from Lavry Engineering titled "20 Bit Equipment For 16 Bit Work?".
It would be interesting to hear comments from the digital audio experts.

Can you hear under the noise floor?

...Reexamination of the frequency plots shows that you can hear a 16 bits dithered signal down to about
-125 dB under full scale.
In the paper, "can" is actually underlined, for emphasis. But what it really means is that you can see it in the frequency plots. Hearing is another thing. Curious how far down Dan Lavry can hear these test signals—"21-bit" is -120.4 dBFS, 22-bit is -126.4 dBFS:

A listening test
...
 
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tuga

tuga

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In the paper, "can" is actually underlined, for emphasis. But what it really means is that you can see it in the frequency plots. Hearing is another thing. Curious how far down Dan Lavry can hear these test signals—"21-bit" is -120.4 dBFS, 22-bit is -126.4 dBFS:

A listening test
...

Maybe he increases the gain so that -120.4 dBFS is raised to -30dBFS?
 

danadam

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Maybe he increases the gain so that -120.4 dBFS is raised to -30dBFS?
No need to exaggerate in the other direction :) I'm listening to some classical now, not particularly loud, and if instead I play =90 dBFS, 3 kHz signal at the same volume, there is no problem hearing it.
 
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