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Sample Rate, Bit Depth and High Resolution Audio

Discussion in 'Sound Science' started by SilentNote, Aug 13, 2019.
  1. SilentNote
    I revisited your initial post and think I misunderstood it the first time round. Are you saying that the interpolation errors are not equivalent to quantization error? Because that is how I understood it when doing my research.

    I was not being condescending. I was genuinely asking those questions, and to point out that if you have not done those hearing evaluations before, now is a good time.

    Let me just say that you cannot assume that everyone by default understands what you are trying to convey. It is more productive to avoid assuming ill intentions of others and clarify any misunderstanding during communication. When it comes to discussing new, and potentially complicated ideas, you cannot fault the listener for not understanding if you have not put in significant effort to make yourself clear, and it is particularly unhelpful to assume that another is simply not open minded. Providing additional links and resources to follow can go a long way to help other people understand the topic. That is of course only if you are genuinely invested to exchange ideas and learn new perspectives.
    Last edited: Aug 18, 2019
    buonassi and Hifiearspeakers like this.
  2. 71 dB
    Quantization by definition breaks linear dependancy of output from input causing nonlinear distortion. However, there is a thing called dithering, which is simple, but damn clever. It randomizes the nonlinear distortion and breaks the correlation between quantization errors and the original signal so that not only does the quantization noise become more pleasant, but the nonlinear distortion gets averaged away and transformed into slightly increased level of quantization noise. So, if you truncate a 24 bit file into a dithered 16 bit file you get this:

    The original 24 bit file + 16 bit noise floor

    You really have this in the dithered 16 bit file as counterintuitive as it is. It's a mathematical fact.

    Now, if this 16 bit noise floor is quiet enough to be inaudible, this sum signal will sound exactly the same as the original 24 bit file itself. Due to the limitations of human dynamic range of hearing, listening conditions and so on, 16 bit noise floor is practically inaudible. In fact, something like 13 bits using normal TPDF dither noise would be just enough for even the most demanding recordings. In comparison the equivalent bit depth of vinyl is 10 bits (~60 dB of dynamic range) at best. However, using shaped dither noise perceptual dynamic range can be expanded by up to 20 dB pushing the perceptual dynamic range of 16 bit digital audio into 110 dB and even more. This is not just more than enough. It's huge overkill. So, 16 bits really is enough (in sound reproduction) and even huge overkill if you use it to it's full potential.
    buonassi likes this.
  3. bigshot
    Well, you don't need to suggest anything. I can tell you that for sure, there is no audible difference between 16 and 24 bit. I've done it many times and always compared the results and it is always identical. I've worked with dozens and dozens of professional sound engineers and none of them could ever hear a difference either. It is very safe to say that the distortions you are talking about are totally inaudible.

    I'm sure you can understand the position of someone who says that they know that 16 and 24 bit have different data in the file, but as long as it sounds exactly the same, it doesn't matter. Who needs better than audibly identical? How many times would you have to transcode between 16 and 24 for this distortion to become audible? 1000 times? 10,000 times? 100,000 times? More? It seems to me in the grand scheme of things, what you're talking about here is one small grain of sand on the entire island of Hawaii.

    The problem with defining more data as being "better" is that more data isn't always better. For instance you can have a super high sampling rate and lots of super audible frequencies present that can't be heard, but it won't necessarily sound "better" when you play it back on your home stereo. Those super audible frequencies might create distortion down lower in the range of human hearing because home equipment isn't generally designed to handle that stuff. The file may be theoretically "better" because it has more information, but it won't sound better. Even assuming your equipment *can* reproduce the super audible frequencies without distortion, it still doesn't sound better... because you can't hear those frequencies.

    There are audiophiles who pursue "better" specs to ridiculous extremes by buying equipment that costs many thousands of dollars more when all it does better is to have smaller numbers on the spec sheet. To human ears, the sound is exactly the same as a mid priced piece of equipment. Is it "better" to have nicer numbers on a piece of paper, or to have more money in your pocket to buy more music? Or more money to buy better speakers, which actually *will* make a marked improvement in sound quality?

    No one here lives in a theoretical world. We all live in the real world. It may be fun to explore "what ifs" and go down absolutist paths purely to entertain ourselves intellectually. But that doesn't help anyone put together a stereo that plays Dark Side of the Moon sounding any better. Pure theory without any grounding in practicality is just as useless as pure ignorance... perhaps worse in fact, because at least with pure ignorance you stand the chance of improving your situation by blind luck.
    Last edited: Aug 18, 2019
  4. TheSonicTruth
    All the higher bit depths do is push the (quantization) noise floor down even further below the ability of people to hear it in the average listening environment. The higher sampling rates help in production, as the audio is put through different processing.
  5. bigshot
    Exactly. When you sit down on the couch to listen to Dark Side of the Moon in your living room, there is absolutely no audible advantage at all... only an advantage on paper. You can play a high data rate lossy file, a CD or a stereo SACD or HD audio... it will all sound exactly the same to human ears.
    TheSonicTruth likes this.
  6. TheSonicTruth
    If the same exact master is used for all three that you mentioned. Tweak the EQ on one or add dynamic compression to the other, and all bets are off, lol!

    Of course, that's what has to be done to the SACD or HD, or the public wouldn't buy it if it sounded exactly the same. All about making money!
    Last edited: Aug 28, 2019
  7. SilentNote
    I realized something today. 20 kHz and above is technically called "ultrasound". I think it might be helpful to start using the actual term instead of 30kHz etc. It would probably be clearer to people when asked: "Are you saying you can hear ultrasound?" than "no one can hear 30kHz." etc.
  8. castleofargh Contributor
    some kids can hear 20kHz, maybe even 22 or 24kHz(at high levels pretty close to pain thresholds). but even they won't care about 30kHz unless we start blasting it directly on their skin or through bone conduction. so the distinction is relevant when discussing "no one can". but in general, for the average human, the 20kHz limit for the audible band was picked for a reason and ultrasounds are more important for our pets ^_^.
  9. SilentNote
    Yea when I was 16 I could hear 21 kHz. I was the 2 students out of the entire class that could hear that in a physics class. Now I can barely hear 17.5 kHz. Hahaha.
  10. bigshot
    Being able to hear super high frequencies isn't an advantage when listening to music. There's nothing to be heard up that high in recorded music, and all there is to hear is high pitched mosquito sounds from old TV sets and bad ballasts on fluorescent lights. I remember as a kid going to a local Sears store that was a huge barn of a building with banks of overhead fluorescent lighting. The sound was painful and made me feel sick. After a couple of years, I stopped noticing it. I didn't realize why at the time. I know now.
  11. old tech
    A while back, some of the local shopping centres were experimenting with playing annoying high pitched 17 khz tones to discourage young teenagers from hanging around the centre. The tones could not be heard by adults (or would be very faint for young adults). It was canned though on the basis that young teenagers are part of society and should not be excluded from hanging around shopping centres.
  12. OmniscientNihilist
    why is frequency response always exactly half of sample rate? and how come when i lower the sample rate (which therefore lowers the frequency response to half) it also lowers the bitrate? is any bitrate WITHIN the remaining part being lost, or just the discarded part?
  13. kinkling
    That doesn't necessarily have to be the case. You can resample from 96 down to 44.1 and not change the bitrate if you so choose.
  14. 71 dB
    The sampling rate says that you have to take samples at least twice the highest frequency in your signal. It's math.

    Intuitive explanation: For example 1000 Hz sinusoidal signal: Such sinewave make one "up" and "down" movement 1000 times a second. In sampling we need to know about every movement up or down and there are 2000 of those together every second so your sampling rate must be at least 2000 (for technical reasons 2200 Hz or so).

    Of course, the frequency response doesn't need to go up to half of sampling rate (for example you can have a CD, sampling rate 44.1 kHz, that has frequencies only up to 15 kHz if your music just doesn't contain higher frequencies. Sampling rate sets the limit what we can do. We can't have 25 kHz frequencies on CD for example.

    Bitrate is how many bits are needed every second. For example CD has 44,100 samples every second x 2 channels of audio x 16 bits per sample = 1411200 bits every second. Now if you half the sample rate to 22.05 kHz, the bitrate is also halfed: 22050 x 2 x 16 = 705600. The frequencies that are too high for the new lower samplerate is discarded (filtered away before downsampling) or if we do nothing folded to the remaining frequency band as distortion.
    castleofargh likes this.
  15. gregorio
    To expand a little on what 71dB stated:

    1. Digital audio is based on a mathematical formula, first published as a theory in 1927 by Harry Nyquist and then proven in 1947 by Claude Shannon. In simple English, the proven theorem is: "If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart." - In other words, provided the analogue signal is limited to half the sample rate, ALL it's properties can be perfectly captured/encoded in digital data and conversely, if the analogue signal is not limited, it's properties cannot be perfectly captured. In practice, if there are frequencies above half the sample rate (called "the Nyquist point") when we encode the signal, we'll end up with mirror images of the signal either side on the Nyquist point, which are called "alias images". The filter used to remove those frequencies is therefore called an "anti-alias filter".

    2. The sample rate is the number of times per second the analogue signal is measured and encoded ("ordinates") in data bits. A sample rate of say 96kHz means that the signal is measured 96,000 times a second, each measurement (ordinate) is stored in (say) 24bits of data. A sample rate of 48kHz means we have half the number of measurements per second (compared to 96kHz sample rate) and therefore half the number of bits per second.

    3. Nothing is lost except "the discarded part", the theorem dictates the signal is "completely determined", not partially determined. In effect, the discarded bits represent the analogue information between the Nyquist Points. So in the example in point #2, the bits being discarded represent the audio frequencies between 24kHz and 48kHz.


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