Volume?
My day-to-day amp has ±48 V rails, and with oscilloscope piggybacked onto the speaker leads I've measured clipping at ±44 V. Man it is loud. I just about never play it that way.
But out of curiosity, I took a very old reel-to-reel tape recording (16 track!) of the Oakland Symphony Orchestra's rendering of Ravel's Bolero out, and played it at "level 10" through the system. The early very quiet section is at least –30 dBW (maybe –40!) below the crashing stuff at the end. This uncompressed raw recording (now long lost in the garage fire) was striking in the huge range it had. (I calibrated what volume level needed so as to not clip at the end, and used that throughout.)
All sorts of musically cogent stuff came forth. In order that the brightest and most powerful passages were not clipped and distorted, the average output power couldn't be higher than –15 dB from peak. [44 × 10–15/20 = 7.7 VRMS ]. The peaks would go close to but never quite hit ±44 V. Cool!
Right there, if the source were not hugely dynamic, but relatively constant, not unlike popular music tracks, that tells me that the average digital values must be only 17.8% of peak. Call it 18%. If 16 bit is ±32768 (value wise), then the average should be [18% of 32768 = ±5,800] or so.
But the next finding (or just "realization") was more of a lightning rod: at say –35 dB for the quiet parts, the signal at the speakers was only [7.7 × 10–35/20 = ±0.139 VRMS ] If 16-bit digital, this is only about ±100 range.
Ah. The bit-noise of ¹/₁₀₀ of the RMS range would be only –40 dB down, and broad spectrum at that. Easily discernable as an underlying hiss. Annoying.
NOTE that the actual level, set to block clipping during the loudest passages, was also too loud to be a reasonable listening level (at the end). I set it to where I liked it one more time, which turned out to be about another –16 dB below its calibration setting. At this setting the loudest parts were only ±1.3 VRMS. If it were from a digitally controlled volume control (i.e. in the digital domain entirely), then we'd be at ±16 countsRMS in the quiet sections! The noise floor would now be –24 dB. Really … not good.
I think this makes a case for 24 bit throughout.
24 bit range is ±8,000,000 (rounded down)
–15 dB volume control setting delivers 1,400,000 count range (–122 dB noise floor)
–15 dB dynamic range (peak to RMS) cuts the RMS count to ±250,000 countsRMS
–35 dB program range for Bolero makes quietest parts ±4,500 counts. Noise floor is -73 dB.
Indeed - if I were to consider the quietest I ever play my system, and if I were to want the amplifier to be driven entirely from the DAC without any resistive or FET volume-controls between (i.e. wide-open, but attenuated digitally to a nice quiet level), of about –50 dB from peak, then Bolero's quietest passages would still have ±100 countRMS range, with a –40 dB noise floor (way below room noise).
Which 16 bit couldn't do, at all.
Voilá!
GoatGuy
Yes? So? I'm getting the feeling that you may not understand the basics of digital recording and playback...
Start by asking yourself how one bit systems work.
Do note that even the best DACs are only capable of 20-21 bits resolution. Having a large bit rate is important if the signal is being heavily manipulated (ie DSP) as round-off errors can significantly reduce the number of bits. These days that is mostly not a problem with the use of 32 bit float.
IMO the sampling rate is more important. And even more important is execution, of both the recording, and the playback.
dave
IMO the sampling rate is more important. And even more important is execution, of both the recording, and the playback.
dave
@goatguy. Clearly you didn't read post #2. I accept that 24 bit processing is handy if you want to do digital volume control. Also good to note that you have discovered crest factor in uncompressed music. But with dithered digital your noise floor is far enough down that none of your concerns actually matter, although people fretted about it in the 80s when CD first came out.
Ooops… you're right, I did miss that in post 2.
And yes, “crest factor” is real, and doing actual metrology to find it - fun!
I'm not sure how much “dithered digital” actually wins in the noise department. It becomes a kind of PWM at the 1 bit level, eeking out another few bits of sub-Nyquist limited resolution. But if you say so, I'm good with it.
And just as you say, once the CD's stream'o'bits is passed thru most CD players' DACs, the unattenuated output then is analog, and just moves through the rest of the system as analog, which isn't particularly impressed by the fact if it were still digital, then a wider word-size would be helpful. Because in analog there is no word-size. Only the analog noise floor.
Which means that we're of the same conclusion intrinsically.
IF one's aiming for a digital-until-final-stage signal path, then 24 bits is wise. IF the DAC is “early” in the signal chain, then 16 bits is just fine. And that's about all one can quantitatively say about it that matters (except for people who love to implement all nature of exotically named, exotically featured and hopefully exotically optimal performance in filtering the signal to yield multiple bandpass-constrained sub-channels, each destined for separate speaker cones in a “multi-amped” configuration).
GoatGuy
PS: could we at least TRY to be a little less snotty? It wouldn't have sullied your Ego to say, “You seem to have missed…”, benefit of the doubt and all that. Jeez…
I'm not disagreeing with you though. I just appreciate more colloquial demeanor, Bill!
GoatGuy
I think the article greatly serves to (unintentionally) highlight the perplexing conundrum of digital audio performance. The author(s) correctly present the largely unimpeachable technical performance of CD standard sampling. With respect to the sensory performance requirements of the human ear, CD is, indeed, essentially perfect sound forever. Yet, the subjective perceieved performance has long been controversial to say the least. For those who may be thinking of doing so, please try to withhold flat declarations that that those who too often feel they hear a CD sound that seems much less than perfect are all necessarily mistaken.
The why, behind the apparent objective-subjective CD performance conundrum has been the subject of much conjecture, both by amateur audiophiles and by professional signal processing scientists. For the record, my current thinking on this is that microphone-feed quality sound is somewhere there in those 16-bit, 44.1KHz samples, it's just that all of the implementation details (of which there are many) must be identified (problem 1), and adequately addressed (problem 2).
Perhaps, the most familiar single example today of such details is jitter. Jitter was of little to no concern in the early years of CD player implementation. My recollection of the only timebase related issue of concern was the long term frequency accuracy of the player's master clock. We now know that jitter can affect human subjective perception of sound quality. Jitter, actually being an analog phenomema, is not included in sampling theory yet it is an important system implementation factor which can prevent perfect signal reconstruction if not addressed. While sampling theory is inescapable perfection, realizing that perfection in a practical physical device has proven far from inescapable, particularly at the affordable prices once expected.
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I'll be more English next time
yeah like we need more Sretens.
In general I think high bit density converters sound much better at lower data rates.
just my subjective observations upgrading from CDs to DVD players or Bluray.
Ive seen similar arguments against high pixel density displays but the market has long ignored them and moved upwards onwards.
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Seriously… once the DAC output wends its way thru the anti-aliasing analog filters (either implicitly designed in, or parasitically there anyway), greater bit-depth is interchangeable with higher sampling rates (provided there's actual interpolation of the samples).
That's because if you have (say) 4× oversampling rate (192 kHz over 48 kHz), you've got four slots which the least bit could be 1 or 0.
1+1+1+1 ÷ 4 = ⁴/₄ = 1.00 binary
1+1+1+0 ÷ 4 = ¾ = 0.11 binary
1+0+1+0 ÷ 4 = ²/₄ = 0.10 binary
1+0+0+0 ÷ 4 = ¼ = 0.01 binary
0+0+0+0 ÷ 4 = ⁰/₄ = 0.00 binary
4× oversampling = log2(4) = 2 bits of resolution dithering.
GoatGuy
(PS: its why your observation works. Greater bit depth at LOWER sampling rates also gives greater resolution)
Guys, I don't understand some things here, could you simplify for my basic understanding please, I believe I'm mixing the concepts:
Let's take a simple TDA1541A : 16 Bits ! 95 dB noise floor. And this thought exercice :
If playing a material of (for instance) 115 dB dynamic behavior,what does it mean ?
Assuming it is a concert event with a relative silence at around 35 dB in the rows but that you can too hear the notes played lower (20 dB for instance). WHere are the limit of the 16 bits with this reccording (imagine it has no post treatment and was reccorded with high dynamic studio stuffs, etc) ?
Is it 115 (reccording) - 95 dB (dac chip)= 20 dB missing : I will hear 20 dB of compression on the peaks ?
Is it 115 - 20 dB (the lowest level hearable in the live event) = 95 dB of dynamic I can only hear during the event (difference is masked at lowest volume by the noise of people in the concert room) ; and so if 95 dB is equal to the behavior dynamic of the chip in relation to its noise floor does it mean I can hear all the 95 dB real dynamic of the concert event in real ? (assuming the dac can drive the speaker and is setuped with zero dB of attenuation to be abble to play at concert level)
Sorry to ask the basic.... assuming the exercice is to listen to at concert level (non amplified= real dynamic behavior of a big concert for instance which can have impressive peaks in milli seconds which make it for me so lively and the hifi borring in relation to the true event).
Thanks you if you can illustrate it in relation to the bit dpth of the dac chip ? (Let say the pre, amp, speaker allow more than 115 dB noise floor to simplify my understanding !)
Let's take a simple TDA1541A : 16 Bits ! 95 dB noise floor. And this thought exercice :
If playing a material of (for instance) 115 dB dynamic behavior,what does it mean ?
Assuming it is a concert event with a relative silence at around 35 dB in the rows but that you can too hear the notes played lower (20 dB for instance). WHere are the limit of the 16 bits with this reccording (imagine it has no post treatment and was reccorded with high dynamic studio stuffs, etc) ?
Is it 115 (reccording) - 95 dB (dac chip)= 20 dB missing : I will hear 20 dB of compression on the peaks ?
Is it 115 - 20 dB (the lowest level hearable in the live event) = 95 dB of dynamic I can only hear during the event (difference is masked at lowest volume by the noise of people in the concert room) ; and so if 95 dB is equal to the behavior dynamic of the chip in relation to its noise floor does it mean I can hear all the 95 dB real dynamic of the concert event in real ? (assuming the dac can drive the speaker and is setuped with zero dB of attenuation to be abble to play at concert level)
Sorry to ask the basic....
assuming the exercice is to listen to at concert level (non amplified= real dynamic behavior of a big concert for instance which can have impressive peaks in milli seconds which make it for me so lively and the hifi borring in relation to the true event).Thanks you if you can illustrate it in relation to the bit dpth of the dac chip ? (Let say the pre, amp, speaker allow more than 115 dB noise floor to simplify my understanding !)
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Eldam,Guys, I don't understand some things here, could you simplify for my basic understanding please, I believe I'm mixing the concepts:
Let's take a simple TDA1541A : 16 Bits ! 95 dB noise floor. And this thought exercice :
If playing a material of (for instance) 115 dB dynamic behavior,what does it mean ?
Assuming it is a concert event with a relative silence at around 35 dB in the rows but that you can too hear the notes played lower (20 dB for instance). WHere are the limit of the 16 bits with this reccording (imagine it has no post treatment and was reccorded with high dynamic studio stuffs, etc) ?
Is it 115 (reccording) - 95 dB (dac chip)= 20 dB missing : I will hear 20 dB of compression on the peaks ?
Is it 115 - 20 dB (the lowest level hearable in the live event) = 95 dB of dynamic I can only hear during the event (difference is masked at lowest volume by the noise of people in the concert room) ; and so if 95 dB is equal to the behavior dynamic of the chip in relation to its noise floor does it mean I can hear all the 95 dB real dynamic of the concert event in real ? (assuming the dac can drive the speaker and is setuped with zero dB of attenuation to be abble to play at concert level)
Sorry to ask the basic....
Thanks you if you can illustrate it in relation to the bit dpth of the dac chip ? (Let say the pre, amp, speaker allow more than 115 dB noise floor to simplify my understanding !)
assumed that the 115 db you mention is the peak level at the time of the recording (db spl), playback with a 16 bit system will indeed result in a noise floor at 20db spl (compared to the situation at the time of the recording.).
Reproducing this (1 on 1) in your environment where you state the quite-level is 35 db spl, Will result in 115 db SPL peak level and some additional noise at 20 db SPL. After some "getting used" to those low SPL levels, you might indeed be able to hear the noise-floor of the DAC.
Only in the softer parts of the recorded material, due to the 16 bits encoding, distortion and resolution will be not too good, because a few bits of the 16 available will be responsible for the sound you'll hear.
So if you want the entire audible range (120 db. OK with pain it goes up to 140db) free from the noise-floor, you'll need about 20/21 bits of encoding. So, then 24 bits reproduction is required.
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Take a look at low level spectra shown in Stereophile's CD and DAC reviews. You can resolve signals well below the LSB. Finding a microphone or preamp with that low of a noise floor is like hunting for unicorns. The 16 bit noise floor is not the noise limitation in any practical system. Remember, the noise is distributed, so each frequency bin will have a much lower noise. Noise shaping drops things even further.
Practical experiment: turn your system up as loudly as you've ever listened to it. Play a silent track. Hear any noise from your seat? I'll bet not.
Practical experiment: turn your system up as loudly as you've ever listened to it. Play a silent track. Hear any noise from your seat? I'll bet not.
Could you clarify the digital signal levels for me?
16bit allows 2^16 = 65536 discrete levels of sampling.
Are those 65536 levels from maximum -ve peak through zero to maximum +ve peak?
i.e. from -32767levels to +32767levels and including zero level? But that loses one level since that adds up to 65535 discrete levels.
Where's the missing level?
Or is it different? Does zero not get allocated a "level"?
16bit allows 2^16 = 65536 discrete levels of sampling.
Are those 65536 levels from maximum -ve peak through zero to maximum +ve peak?
i.e. from -32767levels to +32767levels and including zero level? But that loses one level since that adds up to 65535 discrete levels.
Where's the missing level?
Or is it different? Does zero not get allocated a "level"?
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