5 ms·

Digital Show and Tell (2013): Xiph's Monty on Digital Audio

33 points by anotherhue 2y ago

shmerl 2y ago
A classic. I wish Xiph developed Daala into a fully functional video codec.
112233 2y ago
This is a very infuential video. I often see it referenced when digital audio gets explained. It is also very insiduously misleading in a way that is hard to fault it for. That "band limited signal" that uniquely satisfies Niquist theorem? That is an infinite, periodic signal. No finite (e. g. a song), aperiodic signal can be band limited. That includes any signal with transients. Well, how big is the difference? How much overhead/error/lookahead is needed to approach the Niquist result? It is never mentioned by people referring to this theorem when talking about audio signal sampling! And I wish it was mentioned and explained.
- Kirby64 2y ago
  In practice it doesn't really matter. Most good converters have pretty sharp cutoffs on their anti-aliasing filters, so any aliasing is severely reduced when mixed back in to the converter. Sure an aperiodic signal needs infinite bandwidth to 'accurately' represent it, but you're quickly below the noise floor.
  - 112233 2y ago
    Sure. And having that 2+ kHz headroom surely helps. Still, it is a bit jarring to almost never see reconstruction filter mentioned (except for sigma delta, where you simply cannot ignore it), and always see appeals to Nyquist theorem as a mathematical proof, even though it does not apply. Taking the opportunity, how is the math called that actually does apply to this case?
    - Kirby64 2y ago
      Every ADC/DAC used in audio in existence has an anti-aliasing filter, though. The Xiph video even talks about band-limiting signals with the 21 kHz cutoff filter he shows as the example. It's not talked about, largely, because modern circuit designs already have great anti-aliasing filters that have quite sharp rejection curves.
- amavect 2y ago
  I'd like to answer your questions. While no finite audio clip qualifies as bandlimited, the Nyquist theorem cheats by assuming that the audio clip repeats indefinitely. Doing so results in sharp frequency lines, separated by gaps of zero. Each frequency line lies on an integer multiple of the audio clip's length, the fundamental frequency. Equivalently, every finite audio clip has a time-discrete Fourier transform. Mathematically, an audio clip of length T seconds at a sample rate S Hz must have DFT coefficients separated by 1/T Hz, with a maximum frequency less than S/2 Hz. For example, a 1 second clip at 48000 Hz has DFT coefficients between [0,24000) at every 1 Hz. By increasing the length of the audio clip, the frequency resolution increases. In asking for the error, you ask for the values between the discrete Fourier coefficients. What happens outside of the audio clip determines what happens between coefficients. If the signal repeats, interpolate zeros between coefficients. If the signal goes to zero (not exactly bandlimited), interpolate a sinc function summation between coefficients (this has to do with summation of the rectangular/boxcar function). How much overhead/error/lookahead is needed to approach the Nyquist result? Theoretically, none. But in practice, perfect filters don't exist. In practice, how big is the difference? In order to properly record a real waveform, the signal must go through a physical low-pass filter, or else risk unbounded aliasing. The answer depends on the filter specification. I pulled up a Realtek ALC892 datasheet. When sampling at 44100 Hz, a -1 dB passband at 20158 Hz, and a -80 dB ADC stopband at 24916 Hz. Yep, that allows aliasing to pass through, yet it remains somewhat passable. No surprises from a cheap chip. Hence the importance of oversampling during recording or reconstruction in better chips. The audio files themselves don't need it because the error comes from imperfect filters. https://www.alldatasheet.com/html-pdf/1137676/REALTEK/ALC892/26789/77/ALC892.html https://www.alldatasheet.com/html-pdf/1137676/REALTEK/ALC892... Hope this helps.
  - 112233 2y ago
    It does! Thank you a lot. But I still don't know the name for the hard part (how to quantify the "almost" of the reconstruction filter) Making signal band-limited by repeating it does a nice hat trick: it makes any part of the signal depend on all preceding and all following samples. That effect is not insignificant -- sinc(x) decays as 1/x . This requires that low-pass filter either to generate long pre-ringing tails, or to emit way above the cut-off. I'm sure analog filters have pre-ringing too (by delaying the peak), I just don't know how it is called. But, in short, sampling signal and then reconstructing it causes it to "travel back in time". Trying to limit pre-ringing messes up phase. Nothing in there looks like the ideal iFFT case, and it is hard to find accurate information about all of this.
- steve1977 2y ago
  I think the constraint of using a band limited signal is the big misunderstanding many people have in regards to digital audio. Yes, you can perfectly reproduce a band limited signal as long as the highest frequency is below fs/2. But to get a band limited signal from a “real life” signal without any artifacts can be trickier than one might think. Especially when the Nyquist frequency is near the limit of human hearing. And this is the one big argument in favor of Hi Res audio - moving those filter frequencies high above the hearing threshold.
  - BoingBoomTschak 2y ago
    >And this is the one big argument in favor of Hi Res audio It's really not. For redbook, fs/2 is 22 kHz and while human hearing maxes at 20 kHz, it's not a hard cutoff: combine our low sensibility to high frequencies (cf ISO 226), the average listener's hearing not going much further than 18 in reality and frequency masking by other simultaneous notes and the small aliasing/imaging issues near fs/2 aren't a real problem. But the real important factor rarely mentioned is material: the amount of music with meaningful content at a meaningful volume at those frequencies is statistically negligible. Hi Res audio is snake oil designed to sell the same thing multiple times, period.
    - shmerl 2y ago
      And for higher price too.
    - PrismCrystal 2y ago
      "Hi Res audio is snake oil designed to sell the same thing multiple times, period." The "period" is unwarranted, because there are too important caveats. Firstly, it has been extremely common for albums to be sold with very compressed dynamic range, assuming the average consumer will be listening in noisy environments etc. However, the mastering supplied to Hi Res shops sometimes lacks that compression, so that is where you can hear the album with room to breathe. Secondly, the SACD format allowed adding a layer for 5.1 surround sound. In classical music, this is especially important for works where the performers are spread out around the hall, not just all on stage in front of the listeners. So, with Hi Res the higher frequencies and 24 bit depth are snake oil, but the ancillary benefits are audible to anyone with a good listening environment.

33 points by anotherhue 2y ago

A classic. I wish Xiph developed Daala into a fully functional video codec.

This is a very infuential video. I often see it referenced when digital audio gets explained. It is also very insiduously misleading in a way that is hard to fault it for. That "band limited signal" that uniquely satisfies Niquist theorem? That is an infinite, periodic signal. No finite (e. g. a song), aperiodic signal can be band limited. That includes any signal with transients. Well, how big is the difference? How much overhead/error/lookahead is needed to approach the Niquist result? It is never mentioned by people referring to this theorem when talking about audio signal sampling! And I wish it was mentioned and explained.

Kirby64 2y ago
In practice it doesn't really matter. Most good converters have pretty sharp cutoffs on their anti-aliasing filters, so any aliasing is severely reduced when mixed back in to the converter. Sure an aperiodic signal needs infinite bandwidth to 'accurately' represent it, but you're quickly below the noise floor.
- 112233 2y ago
  Sure. And having that 2+ kHz headroom surely helps. Still, it is a bit jarring to almost never see reconstruction filter mentioned (except for sigma delta, where you simply cannot ignore it), and always see appeals to Nyquist theorem as a mathematical proof, even though it does not apply. Taking the opportunity, how is the math called that actually does apply to this case?
  - Kirby64 2y ago
    Every ADC/DAC used in audio in existence has an anti-aliasing filter, though. The Xiph video even talks about band-limiting signals with the 21 kHz cutoff filter he shows as the example. It's not talked about, largely, because modern circuit designs already have great anti-aliasing filters that have quite sharp rejection curves.
amavect 2y ago
I'd like to answer your questions. While no finite audio clip qualifies as bandlimited, the Nyquist theorem cheats by assuming that the audio clip repeats indefinitely. Doing so results in sharp frequency lines, separated by gaps of zero. Each frequency line lies on an integer multiple of the audio clip's length, the fundamental frequency. Equivalently, every finite audio clip has a time-discrete Fourier transform. Mathematically, an audio clip of length T seconds at a sample rate S Hz must have DFT coefficients separated by 1/T Hz, with a maximum frequency less than S/2 Hz. For example, a 1 second clip at 48000 Hz has DFT coefficients between [0,24000) at every 1 Hz. By increasing the length of the audio clip, the frequency resolution increases. In asking for the error, you ask for the values between the discrete Fourier coefficients. What happens outside of the audio clip determines what happens between coefficients. If the signal repeats, interpolate zeros between coefficients. If the signal goes to zero (not exactly bandlimited), interpolate a sinc function summation between coefficients (this has to do with summation of the rectangular/boxcar function). How much overhead/error/lookahead is needed to approach the Nyquist result? Theoretically, none. But in practice, perfect filters don't exist. In practice, how big is the difference? In order to properly record a real waveform, the signal must go through a physical low-pass filter, or else risk unbounded aliasing. The answer depends on the filter specification. I pulled up a Realtek ALC892 datasheet. When sampling at 44100 Hz, a -1 dB passband at 20158 Hz, and a -80 dB ADC stopband at 24916 Hz. Yep, that allows aliasing to pass through, yet it remains somewhat passable. No surprises from a cheap chip. Hence the importance of oversampling during recording or reconstruction in better chips. The audio files themselves don't need it because the error comes from imperfect filters. https://www.alldatasheet.com/html-pdf/1137676/REALTEK/ALC892/26789/77/ALC892.html https://www.alldatasheet.com/html-pdf/1137676/REALTEK/ALC892... Hope this helps.
- 112233 2y ago
  It does! Thank you a lot. But I still don't know the name for the hard part (how to quantify the "almost" of the reconstruction filter) Making signal band-limited by repeating it does a nice hat trick: it makes any part of the signal depend on all preceding and all following samples. That effect is not insignificant -- sinc(x) decays as 1/x . This requires that low-pass filter either to generate long pre-ringing tails, or to emit way above the cut-off. I'm sure analog filters have pre-ringing too (by delaying the peak), I just don't know how it is called. But, in short, sampling signal and then reconstructing it causes it to "travel back in time". Trying to limit pre-ringing messes up phase. Nothing in there looks like the ideal iFFT case, and it is hard to find accurate information about all of this.
steve1977 2y ago
I think the constraint of using a band limited signal is the big misunderstanding many people have in regards to digital audio. Yes, you can perfectly reproduce a band limited signal as long as the highest frequency is below fs/2. But to get a band limited signal from a “real life” signal without any artifacts can be trickier than one might think. Especially when the Nyquist frequency is near the limit of human hearing. And this is the one big argument in favor of Hi Res audio - moving those filter frequencies high above the hearing threshold.
- BoingBoomTschak 2y ago
  >And this is the one big argument in favor of Hi Res audio It's really not. For redbook, fs/2 is 22 kHz and while human hearing maxes at 20 kHz, it's not a hard cutoff: combine our low sensibility to high frequencies (cf ISO 226), the average listener's hearing not going much further than 18 in reality and frequency masking by other simultaneous notes and the small aliasing/imaging issues near fs/2 aren't a real problem. But the real important factor rarely mentioned is material: the amount of music with meaningful content at a meaningful volume at those frequencies is statistically negligible. Hi Res audio is snake oil designed to sell the same thing multiple times, period.
  - shmerl 2y ago
    And for higher price too.
  - PrismCrystal 2y ago
    "Hi Res audio is snake oil designed to sell the same thing multiple times, period." The "period" is unwarranted, because there are too important caveats. Firstly, it has been extremely common for albums to be sold with very compressed dynamic range, assuming the average consumer will be listening in noisy environments etc. However, the mastering supplied to Hi Res shops sometimes lacks that compression, so that is where you can hear the album with room to breathe. Secondly, the SACD format allowed adding a layer for 5.1 surround sound. In classical music, this is especially important for works where the performers are spread out around the hall, not just all on stage in front of the listeners. So, with Hi Res the higher frequencies and 24 bit depth are snake oil, but the ancillary benefits are audible to anyone with a good listening environment.