additional comments
I have been making the case against higher sample rates for audio for a long time. I have encountered no credible arguments to my paper “Sampling Theory”. The same is true for my recent paper “The Optimal Sample Rate for Quality Audio”. I encounter some that want to counter the message by “shooting the messenger”. Meanwhile the facts I preset are correct and UN-challenged. I realize that reading the papers demands time and concentration. So here is a shorter description of many of the points I presented in the papers. Let’s refrain from diverting the conversation away from the topics.
1. Sampling is not intuitive. SAMPLING IS NOT ANALOGUS TO PIXELS! A more detailed picture may require more pixels, but more audio detail does NOT require more samples. There is an “electronic tool” (filter) that enables recovering ALL of the audio from a limited number of samples. It is not intuitive and requires much study. In fact it is counter-intuitive and goes against “everyday common sense.” This is the reason why the marketing of “more samples is better” is successful in convincing so many of the false notion.
2. Nyquist theorem (theorem is a PROVEN theory) tells us that recovering ALL the audio intact does require the sampling rate (frequency of sampling) to be at least twice as fast as the highest signal (audio) frequency. Theory demands a perfect “reconstruction tool” filter. In practice, real world filters require sampling a little faster than twice the audio bandwidth. For 20 KHz audio bandwidth, the theory requires at least 40 KHz sample rate. The 44.1 KHz standard provides 4.1 KHz margin.
The margin for the filter (from the theoretical filter) is 100*(44.1KHz-2*20KHz)/(2*20KHz) = 10.25%
3. Some people argue that we need more than 20 KHz for audio. The decision as to how wide the audio range is should be left to the ears. Say we agree to accept a 25 KHz as the audio bandwidth. When using 88.2 KHz sampling, (and 25 KHz for the audio bandwidth) the margin is i100*(88.2KHZ-2*25KHz) /(2*25KHZ) = 76.4%.
4. At 96 KHz sampling and 25 KHz audio, the margin is 92%. At 96 KHz sampling and 30 KHz audio the margin is 60%. At 192KHz sampling and 30KHz the margin is 220%!. For anyone crazy enough to claim they hear or feel 40 KHz, when sampling at 192 KHz the margin is still 140%. At 384 KHz sampling the margin is 380%!
5. Some argue that at 44.1 KHz the margin of 10.25% is tight, and that theoretical filters fail to provide a near perfect reconstruction. Others argue that 20 KHz audio is too small to accommodate some ears. Such arguments support some reasonable increase in sampling rate. Many argue that 44.1 KHz rate is good enough. Others disagree. But few will argue with the statement that 44.1 KHz is at least pretty close to acceptable. In order to accommodate those that want improvements, let’s increase the margin by a factor of say 2. You want more, OK, by a factor of 4. You want more audio bandwidth? OK let’s raise it to a factor of 5…
And all that is more than covered by the use of 96 KHz sample rate!
6. A few manufacturers are starting to advocate 384 KHz and even 768 KHz sample rates. When audio sampled at 44.1KHz is considered as being somewhere between “not perfect” and “near perfect”, the notion of sampling 870% faster (for 384KHz) or even 1741% (for 768KHz) faster than a CD makes no sense. I expect even the least competent of designers to be able to design a filter that does not require such huge margins. I would also expect any converter designer to have enough background to know that more samples are not analogous to more pixels! I would expect converter designers to insist that their marketing department knows that, instead of closing their eyes to the crock of steering audio in the wrong direction. I also understand it is not easy when one’s job is on the line.
7. It is not wise to keep increasing the sample rate unnecessarily. The files keep growing, and faster sampling yields less accuracy. Yet the marketing of higher sample rates has no basis, other than some spreading of misinformation. The latest I saw claims that faster sampling yields better stereo location (time resolution). The argument is false. Faster sampling offers the ability to process wider bandwidth, but has no impact what so ever on stereo location!
8. Faster sampling for capturing bandwidth that we do not hear (ultrasonic) is not wise. If we did not hear it (or feel it) we don’t need it. If we did hear it (or feel it) it is not ultrasonic, it is audible bandwidth (by definition). Ultrasonic energy may cause problems by spilling over to the audible range (intermodulation distortions). At best case, ultrasonic energy adds nothing to audio while requiring faster sampling, thus larger files and slower file transfers. In reality there is another price to pay; the faster one samples, the less accurate the result.
Dan Lavry