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This is slightly incorrect. The combination of bit length and sampling rate determine both dynamic range and frequency fidelity. Although it's common to hear t

This is slightly incorrect. The combination of bit length and sampling rate determine both dynamic range and frequency fidelity. Although it's common to hear the two values used to represent these two separate physical measurements, it's just another case of explaining new tech (80s CDs) to old technical consumers (70s hi-fi types). You can measure a reduction in dynamic range by reducing either sampling rate or bit length. You'll frequently find 1-bit A/Ds and D/A at > 5Mhz on high fidelity systems. That 1-bit signal is converted to/from a higher bitrate, lower sampling rate signal without loss of fidelity. If you're interested in looking at alternate bitrate encodings you should just look at the Super Audio CD format https://en.wikipedia.org/wiki/Super_Audio_CD https://en.wikipedia.org/wiki/Super_Audio_CD On your second point, I agree, we live in a noisy world and hearing 144dB of dynamic range would require serious isolation. What most people should be able to hear with 90Dbs of dynamic range, are the harmonics created by undersampling a high frequency signal. To quickly explain I'll use a 1-bit lower frequency scenario. Lets say we have a 2Khz sine wave and a 1-bit 5Khz sampling rate. The 2Khz signal is going to be represented by a different 2 samples every cycle. The result will be a signal that is no longer a sine wave and closer in frequency to 800Hz (wild approximation) than 2Khz. Low pass filters are used to to keep those harmonics from being too pervasive but they still sneak into the signal near the high frequency range. Transpose this example to our current audio standard and you might realize that in order to accurately represent the high end we need a little more than 16bit 48Khz.

badsock 12y ago
In your last example about the harmonics, I can see that being so in the most simple case, but surely that's a limitation of the playback system, not the storage medium. And isn't that addressed by the oversampling that is used almost universally in DACs now?
- ecocentrik 12y ago
  It's a limitation of the recording/storage medium and is addressed by oversampling and low pass filters in ADCs in acoustical recording. Most audio recording, processing and mixing is performed in 24 or 32 bit. Once the data is down sampled for distribution in 16bit 44.1Khz you run into the limitation again where you have fewer samples to represent higher frequencies. The only remedy is to attenuate those frequencies before downsampling. I'm unsure of the role oversampling plays in DACs so I can't speak to that.
  - badsock 12y ago
    My understanding is that oversampling is done in DACs so that digital filters can be applied without introducing the effects that you describe at the top end of the frequency range. Basically it interpolates to a higher sample rate so that there's more play in filter selection/application. In terms of attenuating the high frequencies before downsampling - have I misinterpreted Nyquist? I thought that there was no loss in fidelity, right up to half the sampling rate.
    - ecocentrik 12y ago
      I figured it had something to do with the application of digital filters. There are only two significant samples of a source at half the sampling rate, so it should be able to represent a frequency at exactly half the sampling rate but I can't see how it could accurately represent a frequency at just a few hz below 1/2 the sampling rate. Notice I'm using the word frequency. A sine wave with a frequency of 22,050hz encoded at 16 bit 44Khz is not going to look anything like a sine wave.
      - badsock 12y ago
        Right, 22,050hz looks exactly like a triangle wave on a computer screen. The thing is that a triangle wave is composed of a fundamental sine wave (22kHz), and a series of ascending odd harmonics above it. So after the filters nix everything above 22kHz it looks exactly like a sine wave on a scope. So you're right that you lose information as you go higher in frequency, but there is also commensurately less need for information to recreate it precisely because the filters remove the detail anyway (and if not the filters, the human ear).
        ecocentrik 12y ago
        Sure 22,050hz and 11,025hz get smoothed out into perfect sine waves and the human ear can't hear 22Khz anyway. But the Nyquest frequency isn't some magical threshold that you cross and suddenly everything is perfectly preserved. It's a folding frequency that determines where aliasing is going to occur, or rather where it's not going to occur. A 44Khz sampling rate is based roughly on western tuning (440Hz A) and makes no attempt to accurately capture sounds and frequencies that are not tuned to western music. As you move away from the folding frequency, there are frequencies in the human audible range that can not be represented, so they're discarded or attenuated by anti-aliasing filters. As far as I'm concerned CD audio is outdated tech that most of the world just doesn't care enough to drop. It's ridiculous in a world of 5K retina screens that people can't see the value in higher resolution audio.

badsock 12y ago

In your last example about the harmonics, I can see that being so in the most simple case, but surely that's a limitation of the playback system, not the storage medium. And isn't that addressed by the oversampling that is used almost universally in DACs now?

ecocentrik 12y ago
It's a limitation of the recording/storage medium and is addressed by oversampling and low pass filters in ADCs in acoustical recording. Most audio recording, processing and mixing is performed in 24 or 32 bit. Once the data is down sampled for distribution in 16bit 44.1Khz you run into the limitation again where you have fewer samples to represent higher frequencies. The only remedy is to attenuate those frequencies before downsampling. I'm unsure of the role oversampling plays in DACs so I can't speak to that.
- badsock 12y ago
  My understanding is that oversampling is done in DACs so that digital filters can be applied without introducing the effects that you describe at the top end of the frequency range. Basically it interpolates to a higher sample rate so that there's more play in filter selection/application. In terms of attenuating the high frequencies before downsampling - have I misinterpreted Nyquist? I thought that there was no loss in fidelity, right up to half the sampling rate.
  - ecocentrik 12y ago
    I figured it had something to do with the application of digital filters. There are only two significant samples of a source at half the sampling rate, so it should be able to represent a frequency at exactly half the sampling rate but I can't see how it could accurately represent a frequency at just a few hz below 1/2 the sampling rate. Notice I'm using the word frequency. A sine wave with a frequency of 22,050hz encoded at 16 bit 44Khz is not going to look anything like a sine wave.
    - badsock 12y ago
      Right, 22,050hz looks exactly like a triangle wave on a computer screen. The thing is that a triangle wave is composed of a fundamental sine wave (22kHz), and a series of ascending odd harmonics above it. So after the filters nix everything above 22kHz it looks exactly like a sine wave on a scope. So you're right that you lose information as you go higher in frequency, but there is also commensurately less need for information to recreate it precisely because the filters remove the detail anyway (and if not the filters, the human ear).
      - ecocentrik 12y ago
        Sure 22,050hz and 11,025hz get smoothed out into perfect sine waves and the human ear can't hear 22Khz anyway. But the Nyquest frequency isn't some magical threshold that you cross and suddenly everything is perfectly preserved. It's a folding frequency that determines where aliasing is going to occur, or rather where it's not going to occur. A 44Khz sampling rate is based roughly on western tuning (440Hz A) and makes no attempt to accurately capture sounds and frequencies that are not tuned to western music. As you move away from the folding frequency, there are frequencies in the human audible range that can not be represented, so they're discarded or attenuated by anti-aliasing filters. As far as I'm concerned CD audio is outdated tech that most of the world just doesn't care enough to drop. It's ridiculous in a world of 5K retina screens that people can't see the value in higher resolution audio.