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RE: Bit depths. I am lacking some understanding.

Posted by Tony Lauck (A) on October 14, 2011 at 12:55:03

In Reply to: Bit depths. I am lacking some understanding. posted by kurt s on October 13, 2011 at 20:20:48:

First, what is the S/N ratio of 16 bit? Answer: in reality it is about equivalent to 70 dB S/N ratio with analog. How can this be? We are taught to believe that the S/N ratio of 16 bits is 96 dB. This is not so, from the get go, as about 6 dB is lost from adding dither. Without adding dither then a sine wave at low level disappears suddenly, something that is clearly audible in tail reverberations at the end of a track. So, roughly, the 96 dB is down to 90 dB. Next, the question comes up, what is the peak/average ratio of the loudest part of the music? Answer: this depends on the musical dynamics. The loudest portions of music (e.g. orchestral tutti at FFF) must not peak above 0 dbfs (+32767 or -32768). However if the music has not been compressed, limited or clipped (i.e. is undistorted) the RMS level will be about -20 dB at this point. In other words, one has lost 20 dB of potential S/N ratio because of the need for headroom. The corresponding situation does not apply with analog, because it is possible to exceed the maximum limits and distortion sets in only gradually. It is easily possible to get 70 dB S/N ratio out of a 2 track tape running at 15 IPS, even without any Dolby noise reduction.

Second, noise at -90 dB (which is the best case if one is listening to a carefully adjusted sine wave) is audible in a quiet room when playing orchestral recordings at a natural concert level. Here we have the same problem as before with peak/average signals. If one wishes to listen to the music where FFF passages have an SPL of 85 dB the peaks are going to be at 105 dB. Thus the dither noise will be at 15 dB, clearly audible. (If you want to snipe at the numbers, then I will just move a bit closer, e.g. the level at the conductor's podium will certainly reach 90 dB and so the peaks are up to 110 dB and the noise at 20 dB.)

So 16 bits is simply not enough for playback of orchestral music. The situation is even worse when making live recordings, since the engineers have no exact idea how loud the musicians are going to play, and hence are going to have to "waste" one or two bits or run the risk of ruining at tape with horrible ugly digital clipping distortion. Now one may say that ADCs and DACs aren't accurate to more than about 20 bits, so there is no need for 24 bits. Here there are two responses: first computer words are organized in multiples of 8, so it is logical to go to 24 bits. Second, if data is to be processed (unfortunately this means most recordings) there will be multiple gain changes, equalizations, mixes, etc. and there will be bits lost in the processing. Hence the need for "guard" bits. This takes us soundly up to 24 bits. Twenty-four bits are clearly useful in studio production processes and so chips and cards have been developed to handle these word lengths.

The next question is: do these converters actually provide 24 bits? At present, the best chips are almost there in terms of their specifications, especially the best DAC chips. Contrary to popular belief, there is no physical limit on the possible noise out of a DAC, other than that created by the dither noise (roughly -138 dBfs) out of a 24 bit DAC. The obvious limit that you mentions is noise in the output converter circuit. This depends on the temperature, bandwidth, and impedance of the signal. The bandwidth is limited (and conventionally noise is weighted due to audibility to the 0 - 20 kHz band). One is probably not going to use liquid nitrogen to cool the chips, so the temperature is fixed. However, their is no limit to the output impedance. One can get a low output impedance by running multiple switches in parallel. We see this in the ESS SABRE chips where their S/N ratio is better when the chip is run in stereo mode, and one of the reasons is that the output circuitry ends up with a lower impedance.

Now it may be that other components in the system don't have a suitable signal to noise ratio. (This is most likely the case at the front of the recording chain, e.g. the microphones or microphone preamplifiers.) But this is hardly an excuse to justify lower performance elsewhere. I've lots of experience with this "good enough" philosophy. It can work well from a business perspective for a while, since there will be no obvious benefits from making all the links in a chain stronger until the last one has been beefed up. But eventually a competitor will come along and do all the necessary homework and the original company will find themselves relegated to the dust bin of history. (There are microphones and microphone preamps that approach 140 dB S/N ratio, but only when used up close on very loud sources.)

This leaves the question of 32 bits, i.e. Why more than 24 bits? Here there is a simple reason: "Why not?" It may not help, but it's not going to cost much, either. If one is processing 24 bit data in the computer, be it a gain change or resample, there will be additional bits generated and so it won't cost anything to keep extra bits and send them to the DAC, assuming the I/O scheme has sufficient bandwidth. When the DAC gets these bits it's going to have to convert them to a higher sampling rate and this is going to use at least 48 bit arithmetic if the upsample quality is at all decent. It costs a few extra stages in a shift register and gates in a multiplexor to allow 32 bit input, and that's it. So the benefit may be minimum, but so is the cost. (The best DAC chips are approaching 24 bit resolution, and this means that they will see a slight increase in resolution from starting at 32 bits instead of 24 bits, perhaps half a bit worth, so the minute extra cost makes sense from a marketing perspective. This will show up on a DAC chip spec sheet, even if the vendor is completely honest in their numbers.)

People have heard differences between 32 bit audio converted to 24 bits with and without dither. Or so they say, and some of the people are careful, consistent and credible. So there is a possibility of a slight gain, enough to justify a few software instructions and gates. Whether it justifies storing 33% more bits on disk is debatable, but that's a choice that can be made recording-by-recording if the equipment allows.

Tony Lauck

"Diversity is the law of nature; no two entities in this universe are uniform." - P.R. Sarkar

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