Noise, Resolution & Benchmark Resolution and Dynamic Range

Sidebar: Resolution and Dynamic Range

When you add more bits to a digital format, you add more potential volume levels. A 16-bit system has 65,536 unique levels; a 24-bit system increases that 256 times, to 16,777,216 levels. It seems reasonable, then, to use the word resolution to describe what you gain when you add more bits.

Apparently, though, it isn't. Benchmark's John Siau told me in an e-mail exchange that if a digital system is properly dithered, those discrete levels don't really exist—and on further thought, it makes sense. "If the digital audio is TPDF dithered"—TPDF stands for Triangular Probability Density Function, the best kind of dither—"the bit depth determines the SNR of the digital channel but does not limit the 'resolution' or number of 'volume levels,'" Siau wrote. "It is precisely equivalent to adding random noise to the analog input. No distortion is added and no audio details are lost. Very-low-level musical details still exist and can be seen on a spectrum analyzer. These details may be masked by the noise, but this is exactly the same thing that would happen if the same amount of noise was added in the analog domain. When TPDF dither is properly applied, a piano decay will sound just like the original, but with added noise. The bit depth of a TPDF-dithered digital channel determines the channel SNR and nothing else."

In contrast, "if the digital audio is not dithered, the volume levels are quantized and small signals can disappear entirely. Larger signals will be distorted by the quantization. The distortion will be a combination of harmonic and intermodulation distortion. If dither is not used, a piano decay will sound distorted and will end abruptly." Essentially, all music recorded digitally, for at least 30 years, employs dither (footnote 1), either intentional or—for high-resolution recordings—naturally occurring in the form of thermal noise (footnote 2).

"I like to do 8-bit demonstrations where I play a 3kHz tone that is 30dB lower than the dither noise," Siau continued. "The SNR of an 8-bit TPDF system is only 45dB, but our ears can hear a 3kHz tone at –75dBFS in an 8-bit TPDF-dithered system. An FFT analysis shows that the –75dBFS tone is distortion-free."

Resolution, then, is not the right word for what you lose when you reduce the bit depth of a properly dithered audio signal. A much more apt term is dynamic range.—Jim Austin



Footnote 1: Early digital recordings weren't properly dithered, if at all. A notorious example is Ry Cooder's Bop Till You Drop, recorded on an early 3M machine and released in 1979 on LP.—John Atkinson

Footnote 2: Actually, as Stanley Lipshitz once demonstrated at an AES convention, analog thermal noise doesn't act as dither unless it is at the appropriate level. Higher than that level and it is just part of the analog signal to be digitized.—John Atkinson

COMMENTS
rt66indierock's picture

With my first office system I had no noise at idle but substitute the Klipsch Hersey's from my home system and I could hear noise at idle.

My office is pretty quiet. Currently 36 to 39 dB with a "river" running underneath it. Without the river at night 24 to 28 dB.

Last year an acquaintance brought his Brenchmark DAC and Amp in with Joseph Audio Pulsars. We noticed and then measured a small difference in the dynamic range of his system and mine. So good job.

John, I'll take "Down in Hollywood" exactly as the 3M machine recorded it. See you Friday.

JimAustin's picture

I'm very curious about your river. I've thought about it and can't figure it out--unless you live on the Pacific coast and over a sea cave. Or something.

rt66indierock's picture

The Phoenix Mountains Preserve is less than two miles away and when it rains like it has the last 72 hours (3.43 inches) a large amount of water flows down the mountains to the flood control canal creating a river.

This river runs under my office into to the flood control canal next to it. I was curious how much extra noise it created so I measured it. Actually not much extra noise.

Nothing left of the river today but it is a regular part of our monsoon season.

Bogolu Haranath's picture

"A River runs Through it" .............. Mark Isham :-) ...........

ok's picture

..but I wonder whether the same or similar listening remarks (since we’re not talking highly differential observations here) wouldn’t have also been possible by using various random configurations for whatever reasons unrelated to real bit depth or THD+N. In my opinion any kind of electronic THD under 0,1% or so is musically meaningless at best (especially when achieved by means of excessive negative feedback which is related to other forms of distortion) mainly due to speaker's erratic frequency response and harmonic distortion bottleneck; pretty much like trying to bypass nearsightedness by increasing screen contrast. However higher figures of electronic THD could arguably accumulate to or even compete certain speaker distortion patterns with rather unpredictable results.

JimAustin's picture

..but I wonder whether the same or similar listening remarks (since we’re not talking highly differential observations here) wouldn’t have also been possible by using various random configurations for whatever reasons unrelated to real bit depth or THD+N.

Yes, that is possible. It would be exceedingly time-consuming to rule out that possibility.

In my opinion any kind of electronic THD under 0,1% or so is musically meaningless at best (especially when achieved by means of excessive negative feedback which is related to other forms of distortion) mainly due to speaker's erratic frequency response and harmonic distortion bottleneck; pretty much like trying to bypass nearsightedness by increasing screen contrast. However higher figures of electronic THD could arguably accumulate to or even compete certain speaker distortion patterns with rather unpredictable results.

I was, frankly, surprised to hear a difference. And while it was obvious once identified, it's not something you'd notice in casual listening--regardless of whether or not it correlates with THD+N. This is very close to what I set out to test--though, as my answer to your first question acknowledges, the test is more suggestive than definitive. Maybe the obvious conclusion from this experiment is that the kind of numbers Benchmark has achieved are most useful in the studio--and especially at the conversion stage, where there may be several conversions. In a studio, a power amplifier is used for monitoring only--so, a single pass. The AHD-2 is a great amplifier, but unless the differences I heard are indeed attributable to distortion and noise, I don't know why anyone, even a studio, would need an amplifier that clean.

JimAustin's picture

I thought I should add, having just rewritten what I wrote a few weeks ago: I'm convinced that noise is not responsible for the differences I heard. I'm convinced that, as I wrote, if you can't hear noise, noise is not a problem; after all, you can hear through noise. I'm far less convinced about distortion. Distortion, correlated with the music, can obscure detail. At what level, I'm not sure.

ok's picture

..I've also heard this amp; it sounded truly remarkable – and I don't mean merely on the detail department.

Ortofan's picture

... "excessive" negative feedback:
https://linearaudio.net/sites/linearaudio.net/files/volume1bp.pdf

ok's picture

of Bruno’s views on a handful of matters and as far as I know he’s not a proponent of feedback excess in non-class D amplifiers. In this very paper (p. 14-15) he clearly states that his use of excessive NF in conventional amps is purely experimental and mostly unstable, while “normal” amounts of global feedback admittedly render their sound somewhat unpleasant (well, not that I'd personaly reject any amp merely on feedback grounds). By the way his class D amps and active speakers tend to sound arguably better than some 90% of the current hi-end circulation.

Bogolu Haranath's picture

Manufacturers of conventional SS amps like Ayre and Pass use almost no NF ........... Two examples ........

dalethorn's picture

When it comes to power amps, I think it's foolish to skimp on anything. If it doesn'r weigh at least 300 lbs and raise the room temperature noticeably, it's too weak.

Ortofan's picture

... negative feedback (as it applies to electronic circuits), perhaps you can quantify the amount of negative feedback that you deem to be "excessive" and describe how you make that determination?

ok's picture

should be considered within context, not per se. Compromises usually need to be made between low THD+N, wide bandwidth, high damping factor pros and gain drain, higher order distortion pattern, brick wall clipping etc cons. Class D amplifiers may need more than 30 db of global feedback to effectively operate, while some class A/B ss or tube designs are doing all right with just 3 db bordering to none. There are also power amplifiers (CH Precision comes to mind) that allow the end user to swap between global and local feedback depending on speaker impedance and personal taste. Your question, if not teasing, otherwise reminds me of the ancient greek “sorites paradox” which seeks to determine the exact point where accumulated grains of sand actually become a heap.

Bogolu Haranath's picture

Some tube amp manufacturers provide user adjustable feedback controls .......... Cary Audio is one example ............

Ortofan's picture

... amplifier. How do you determine whether or not a given amp employs what you refer to as an "excessive" amount of negative feedback?

ok's picture

..THD and damping factor; if it works, I don't mind.

Ortofan's picture

... do you want an amp to have?

ok's picture

..above 20 something is actually marketing overkill. When cable/crossover/voice coil is taken into account, there is no such thing as a DF of 1000. I've heard zero-feedback amp with a measured DF of 18 that handled bass with Darth Vader force grip; same figure in a feedback-based amplifier would arguably suggest an embarrassing piece of junkware.

Ortofan's picture

... that audible variations in frequency response won't be introduced when such an amp is used with a speaker having a non-linear impedance?

ok's picture

and even measurable to a certain degree, though it actually depends on many a factor (output devices, power supply, bias current, signal path etc) amongst which nominal output impedance is probably the least significant one. In general I find speaker measurements (please someone add distortion figures!) far more straightforward and informative than the electronics counterpart, the actual meaning of which remains in many a case rather obscure. Or, as Putzeys puts it (referring to MQA): “Meanwhile I'm happy to do speakers. You wouldn't believe how much impact speakers have on replay fidelity”.

Bogolu Haranath's picture

Putzeys designed Kii Audio Three loudspeakers using his Class-D internal amplifiers ........ The speakers are listed under Class-A Stereophile ............

Bogolu Haranath's picture

Nelson Pass talks about amplifier design in an article published by Stereophile .......... That article can be found at Stereophile References ..........

Ortofan's picture

... are you then willing to accept as a by-product of using an amplifier with a relatively lower damping factor (or higher output impedance)?

ok's picture

since I already own a decade old, modestly powered, zero feedback integrated combined with some 88db/m, mostly 4 to 3 ohms, almost flat 35Hz-20KHz response (all according to third party actual measurements) 3-way floorstanders and I can attest that the results are nothing less than extraordinary from whisper to shout for any casual city dweller. Cables are of crucial importance but nothing really extravagant. Never mind names and prices – not to be found at Recommended Components either.

Ortofan's picture

... the fabled mystery amp and speakers.

Their performance is always described as "extraordinary" when the make and model of the equipment somehow can't be revealed.

ok's picture

..but it was just an interview, not an advertisement as your average posts.

Ortofan's picture

... the Socratic method won't succeed.

ok's picture

..the aforementioned speakers are favorably presented in JVS’s latest RMAF report driven by some tube integrated. Measurements are easily accessible through the net I suppose ;-)

jeffhenning's picture

So the amp with the greatest linearity, least noise and least distortion might not be the most resolving, truest amplifier?

Sorry, but that seems nonsensical. Are you sure your speakers are really up to the task? Sorry again, I don't think they are.

I'll closely paraphrase Benchmark's John Siau in what he wrote me 3 years ago (my memory is not photographic): "When you first hear an amp like the AHB2 if you are used to amps with more noise and distortion, the AHB2 may sound wrong. Given some time, that fades. In the end, the superior amp will sound always better."

JimAustin's picture

Can't help thinking you didn't read the article, or not carefully.

Bogolu Haranath's picture

HR wrote an interesting article about loudspeakers, which was recently published on the AudioStream website ....... Interesting article and interesting comments :-) ..........

Solarophile's picture

So what did HR say that was of any relevance here? As usual, I found his thoughts rather vague in that article.

Bogolu Haranath's picture

May be the loudspeakers are the weak link? :-) .............

Solarophile's picture

Speakers and headphones are always the weakest link compared to any decent DAC or amplifier whenever we start comparing things like distortion.

Robin Landseadel's picture

No LP playback will ever have s/n ratios like these. Kinda hard to think of LP reproduction being "high resolution" in this context.

Bogolu Haranath's picture

The SNR of vinyl LP is approx. 50-55 db ........... which is approx. 8-10 bits .........

Bogolu Haranath's picture

The SNR of analog reel to reel tape is approx. 72 db, which is approx. 12 bits ...........

Bogolu Haranath's picture

The SNR of analog cassette tape is approx. 63 db, which is approx. 10 bits .........

Bogolu Haranath's picture

The SNR of DAT is approximately the same as CD .............

Bogolu Haranath's picture

Nagra makes a digital reel to reel audio tape machine (the company says is) capable of recording in 24/96 resolution ..........

Bogolu Haranath's picture

JA recorded "Duet" album with a Nagra-D digital tape recorder at 24/88.2 resolution using "Decca Tree" 3 microphone configuration ..........

dalethorn's picture

I'm still waiting on a definitive list of "Decca Tree" recordings, with all of the facts in one list. I'm so busy arresting immigrants these days that I don't have time to build my own list from scratch.

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