All Digital Audio Articles are Flawed.
I've been doing a bit of reading on 16bit vs 24bit audio and came across this article that claims 24bit/192kHz playback is basically pointless (but, that's not what I'm hear to discuss).
There is endless online debates on virtually all aspects of digital audio, and articles as the one you have cited are common triggers.
The reason is that all these articles are flawed and incomplete. There are 3 reasons for this:
- Digital audio theory is complex - I've been teaching digital audio for years, and can assert that it takes about 60 frontal hours of teaching to only cover the topic on a fundamental level. Authors of articles can not provide such vast amount of information, thus the explanations are always incomplete.
- Authors are often biased and pointing - Most authors try to argue a certain thing, but they choose not to show the cases which will object their arguments. Authors can guard their argument by carefully picking terms, so the argument itself is reasonable and logical. But you can easily be misled to believe A also means B, but B was never actually mentioned. For instance, it may justified to say that it is pointless recording at 192kHz, but only if the audio is never to be processed in the digital domain (there are benefits processing at higher sample rates and higher bit depths). The point is that "recording" does not mean "processing", so the statement "it is pointless to record at 192kHz" is reasonable, but it still doesn't mean there are no benefits in doing that.
- There's an undetermined gap between theory and practice - People's opinion is often subdivided on the theoretical and practical levels. The theorists will claim that any issue, audible or not should be accounted for; The practical ones claim that issues should only be accounted for if audible and distinguishable. The problem is that whether or not issues will be audible depends on countless variables that change on a case basis - so whether or not 16 bit will be audibly distinguishable from 24 bit depends on the signal being processed, amount and nature of the processing, the monitoring setup, to name a few. So it's anyone's guess really.
Resolution in Digital Audio
What I found surprising was the fact that moving to a 24bit recording process doesn't result in a higher resolution per sample, but rather a wider dynamic range.
The term resolution is nearly always misused in the context of digital audio. Digital audio books use the term to describe "the amount of information" we have on something. This may apply to the resolution of frequency spectrum analysis, which can be done at lower or higher resolutions.
But if applied directly to digital audio, the word means "the amount of information we have on the signal". In that context, it is perfectly correct to say (from The Scientist and Engineer's Guide to Digital Signal Processing):
"An analog signal formed from frequencies between 0Hz and 10 kHz will have exactly the same resolution as a digital signal sampled at 20 kHz."
Perhaps surprisingly, sampling theory does not account for dynamic range - the theory states that as long as a signal is sampled at equal intervals at least twice as fast from the highest frequency present, the signal representation is perfect and complete - that is, we have all the information we need to recreate the signal.
But what about dynamic range you may ask? By the sampling theorem, digital audio has infinite sampling range. However, the practice of rounding (quantising) continuous analogue voltage to discrete digital values yields an error, and this error translates to noise, and this noise determines the signal to noise ratio of the system, which most people consider the dynamic range of the system (which is not perfectly correct as depending on the frequency content we can hear sounds below the noise floor; it depends whether you define dynamic range as physical or perceptual phenomenon).
Now could you say that a digital audio with a higher bit depth has more resolution? It is certainly tempting, but here is the catch:
A 1 bit ADC at very high sample rates will yield a higher Signal-to-Noise ratio (thus dynamic range) than 24 bit ADC at very low sample rates.
In fact, nearly all modern ADCs are built with 1-bit Delta Sigma converters in them. Whether you choose 16 or 24 bits, and whether you choose 44.1 or 192kHz, the converters first sample with 1 bit at high sample rates, only then convert it to your choice of format.
So what is resolution really? Nika Aldrich brilliantly explains it in his book Digital Audio Explain for The Audio Engineer:
Until now the term "resolution" has not been used in conjunction with bit depth of digital recordings in the book... The term "resolution" implies a subjective measure of quality... There are, however, only four characteristics of a waveform.. "Resolution" is not one of them.
Digital Audio is not Digital Photography
I would have assumed this to work in a similar way as digital images.
The analogy between the two is intuitive, in fact it would be weird if people didn't make it. But digital audio and photography are not the same, not in the core at least. In fact, the analogy to camera sensors is a prime reason to why people fail to grasp digital audio.
Digital sensors involve 1 sample (of varying intervals) of a matrix of pixels - otherwise, one sample with many measurements. Digital audio involves many samples of equal intervals over time, each made of a single measurement. The process is not the same.
Resolution in digital photography equates the number of pixels per image. But higher resolution (more pixels) in digital images does not necessarily mean higher quality - higher resolution sensors mean the matrix is made of smaller pixel sensor, so less photons hit each pixel sensor, which yields more noise. This is what Apple is trying to convince people:
Digital audio does not conform to the same principles. More bits to describe a sample simply mean less rounding, so less noise. But this is not the same as the noise we talk about with photography.
You are correct making the comparison between colour depth (8 or 16 bit per channel), to bit depth in audio. But neither noise or resolution is part of this.
Dynamic Range in Digital Audio
To begin with, all ADCs are calibrated to a specific window of input voltage. For simplicity, lets consider the range to be -1V to +1V. Regardless of the sampling bit depth (24 bit, 16 bit, or 1 bit - which is what is actually used internally) the voltage measurements are always taken for the same voltage range.
Now imagine you have to map 1 bit into this range. You have two step (quantas) - 0 and 1. It would be sensible to put these at -0.5V (0) and +0.5V (1).
Now if you pick arbitrary input values and round them to the nearest step, you'll see the error will never be higher than 0.5V. For instance, an input of +1V will be rounded to +0.5V. This rounding generates noise, and the noise highest peak can be at +0.5V (the maximum rounding error).
If we now use 2 bit sampling, we get four quantisation steps: -0.75V (0), -0.25V (1), +0.25V (2), +0.75V (3).
This time the maximum rounding error is 0.25V, so the quantisation noise highest peak will be at 0.25V - half of that with 1 bit conversion.
So every time you add a bit, the quantisation noise level halves.
As previously explained, we consider the signal to noise ratio as the dynamic range of the system.
