Nyquist-Shannon; The Backbone of Digital Sound

[Dawnshine Wonder 2,704]

Was the Nyquist Shannon theorem correct on CD audio? yes. Unfortunately audio recordings are not perfect and have to be filtered. This is why oversampling is needed, from what I learned about this by looking this up online, you also have to take into account things like quantization noise. But from what I researched so far, I learned with a sufficiently suppressed noise floor, 96db dynamic range is plenty. Some people claim they can hear above 20khz frequency but that has not been scientifically proven, worse, as we get older, that range of hearing gets reduced. For the finished product, 44.1khz 16bit is spot on, this is why the redbook CD standard has held up. But with content creation, it gets more complicated, and that is best done by professionals, not me.

 

 

[Pentium100 2,294]

On 2025-03-15 at 6:39 PM, Dawnshine Wonder said:

Unfortunately audio recordings are not perfect and have to be filtered. This is why oversampling is needed, from what I learned about this by looking this up online, you also have to take into account things like quantization noise.

For the conversion to digital to work, there has to be nothing above the half sampling rate. If there is, you get aliasing which sounds bad. Basically, with a 40kHz (I know, non-standard, but it made the math easier) sampling rate a 18kHz signal and a 22kHz signal will produce the same exact samples and will be reproduced as 18kHz.

Its the same effect when a spinning wheel seems to be stationary or spinning backward when filmed depending on the speed and frame rate.

So, we need to filter the incoming signal so there is nothing above the half sample rate. So, a sample rate of 40kHz is out - there is no way to make a filter that will pass 19.999kHz and completely block 20.001kHz, so a sample rate of 44.1kHz was chosen. Why such a weird number (and not, say, 45kHz)? Early digital recordings were made with PCM converters and recorded to video tapes and the frequency was chosen as it worked with the frame rate/line rate of both 50Hz and 60Hz systems. 48kHz was chosen for DAT as it made the filter design a bit easier (and maybe to intentionally make it incompatible with CDs though most DAT decks can also record at 44.1kHz).

Anyway, with 44.1kHz, you need a filter that passes 20kHz, but block 22kHz, which can be done and was done, but it is not great, as such a steep filter will have fluctuations in the pass band. One way to make it better is to increase the sample rate. With 96kHz, you need a filter that passes 20kHz, but blocks 48kHz, this can be done much more easily.

Another way is to oversample. Incoming signal is sampled at the higher rate, then it is digitally filtered (easier to make a steep digital filter than an analog one), then converted to the lower sample rate. 

During playback you need the same filter on the output. Otherwise, a 18kHz signal recorded at 40kHz sample rate will produce 18kHz, 22kHz, 38kHz, 42lHz etc. Again, for a lower sample rate recording, you can resample to a higher frequency, filter it digitally then convert it to analog and use a simpler analog filter.

Resampling is a simple process if you want to increase or decrease the sample rate by 2x, 3x etc. Resampling from 44.1kHz to 48kHz is more involved and loses more quality. I do not know how it is now, but in the past simpler PC sound cards ran the DAC at 48kHz and resampled everything else. A better sound card can run the DAC at different frequencies, depending on the source. Even now, even if the sound card can do it, Windows or Linux may want to resample, unless you specifically use programs that allow "bit perfect" playback. 

In reality, there is some weirdness with DACs at 44.1kHz as I have recently found out trying to make a CD with test signals so I could calibrate my tape deck easier without having to connect a function generator every time I wanted to do that.

[Dawnshine Wonder 2,704]

18 hours ago, Pentium100 said:

For the conversion to digital to work, there has to be nothing above the half sampling rate. If there is, you get aliasing which sounds bad. Basically, with a 40kHz (I know, non-standard, but it made the math easier) sampling rate a 18kHz signal and a 22kHz signal will produce the same exact samples and will be reproduced as 18kHz.

Its the same effect when a spinning wheel seems to be stationary or spinning backward when filmed depending on the speed and frame rate.

So, we need to filter the incoming signal so there is nothing above the half sample rate. So, a sample rate of 40kHz is out - there is no way to make a filter that will pass 19.999kHz and completely block 20.001kHz, so a sample rate of 44.1kHz was chosen. Why such a weird number (and not, say, 45kHz)? Early digital recordings were made with PCM converters and recorded to video tapes and the frequency was chosen as it worked with the frame rate/line rate of both 50Hz and 60Hz systems. 48kHz was chosen for DAT as it made the filter design a bit easier (and maybe to intentionally make it incompatible with CDs though most DAT decks can also record at 44.1kHz).

Anyway, with 44.1kHz, you need a filter that passes 20kHz, but block 22kHz, which can be done and was done, but it is not great, as such a steep filter will have fluctuations in the pass band. One way to make it better is to increase the sample rate. With 96kHz, you need a filter that passes 20kHz, but blocks 48kHz, this can be done much more easily.

Another way is to oversample. Incoming signal is sampled at the higher rate, then it is digitally filtered (easier to make a steep digital filter than an analog one), then converted to the lower sample rate. 

During playback you need the same filter on the output. Otherwise, a 18kHz signal recorded at 40kHz sample rate will produce 18kHz, 22kHz, 38kHz, 42lHz etc. Again, for a lower sample rate recording, you can resample to a higher frequency, filter it digitally then convert it to analog and use a simpler analog filter.

Resampling is a simple process if you want to increase or decrease the sample rate by 2x, 3x etc. Resampling from 44.1kHz to 48kHz is more involved and loses more quality. I do not know how it is now, but in the past simpler PC sound cards ran the DAC at 48kHz and resampled everything else. A better sound card can run the DAC at different frequencies, depending on the source. Even now, even if the sound card can do it, Windows or Linux may want to resample, unless you specifically use programs that allow "bit perfect" playback. 

In reality, there is some weirdness with DACs at 44.1kHz as I have recently found out trying to make a CD with test signals so I could calibrate my tape deck easier without having to connect a function generator every time I wanted to do that.

Resampling does suck, however without high quality gear it doesn't matter. Very few media players support bit perfect playback in Windows from what I noticed. Media Monkey does, so does Jriver. But it's not supported in Winamp or Windows Media Player Legacy, or Groove. I don't know if it's supported in Foobar2000 or MusicBee but last I checked VLC player it was not. As far as I know, for bit perfect audio output, we need an app which supports either ASIO or WASAPI exclusive mode. ASIO is also dependent on if our audio device supports it, motherboard audio often doesn't. But you get what you pay for, which goes back to the 100$ DAC thing I mentioned in a different thread. But there is a limit to what external DACs are able to do, the rest is up to your amplifier all the way up to your headphones.

 

Some people claim accurate PCM requires an R2R DAC, an old technology much like tube amps, but I have not seen any evidence related to double blind tests which prove that R2R is objectively better than Delta Sigma. People claim R2R is better but I bet most of them could not tell the difference if they compared them in a fair test. At least that's what AudioScienceReview indicates, Amir also knows what he is talking about. A Youtube video is not a fair test of either of these DAC types, as lossy compression destroys any detail which would have made this possible, so people cannot judge the differences with that. No matter how it processes the signal, what matters is if the differences are audible to human ears, and if they are not, then the claimed differences beyond that is generally regarded as a scam or marketing hype IMO.

 

 

[Pentium100 2,294]

5 hours ago, Dawnshine Wonder said:

Very few media players support bit perfect playback in Windows from what I noticed.

Yeah, it's easier on Linux. 

Foobar2000 supports it on Windows though.

5 hours ago, Dawnshine Wonder said:

Some people claim accurate PCM requires an R2R DAC, an old technology much like tube amps, but I have not seen any evidence related to double blind tests which prove that R2R is objectively better than Delta Sigma.

Without oversampling, maybe, with oversampling, it should be very close. IMO more important would be the analog portion of the DAC. 

[Dawnshine Wonder 2,704]

On 2025-03-20 at 9:52 PM, Pentium100 said:

Without oversampling, maybe, with oversampling, it should be very close. IMO more important would be the analog portion of the DAC. 

That's a good point actually, I've heard it said many times and it is true that if the DAC doesn't have sufficient isolation and grounding, then electromagnetic interference would cause problems with it. This is why noisy environments like inside a PC can affect the quality of the output, which does affect the analog portion of a DAC. The whole point of going to an external DAC besides just the amplification. DACs can be separate units entirely from an amp I am aware, but many DAC products come with their own built in amplifier. HiFi enthusiasts tend to not want to rely on motherboard audio for that reason. It's not that it doesn't have enough amplification, motherboards can come with decent headphone amps built in which can drive headphones with at least moderate impedance and sensitivity levels, but unless they're well isolated from other components it kind of defeats the purpose.

[Pentium100 2,294]

10 hours ago, Dawnshine Wonder said:

DACs can be separate units entirely from an amp I am aware, but many DAC products come with their own built in amplifier.

A DAC has to have some kind of amplifier to make the output have normal level (0.775V or whatever) and have reasonably low output impedance so that you can connect it to the amplieifer or whatever.

10 hours ago, Dawnshine Wonder said:

HiFi enthusiasts tend to not want to rely on motherboard audio for that reason.

Motherboard audio will usually have lower quality for multiple reasons -

• the space is limited - compare to the size of a sound card to the portion of the motherboard dedicated to audio.
• less screening/isolation - in part due to lack of space, in part due to cost
• lower quality DAC and its analog circuits- to save money, as not everyone who buys the motherboard cares that much about sound quality, so why make it more expensive?

An external audio interface would be better, whether using USB or a DAC/ADC that is connected using a digital interface (if you use optical, you can even avoid ground loops).

[Dawnshine Wonder 2,704]

15 hours ago, Pentium100 said:

An external audio interface would be better, whether using USB or a DAC/ADC that is connected using a digital interface (if you use optical, you can even avoid ground loops).

The added benefit of external DAC is XLR balanced which is excellent. On short cable runs it's not so much of an issue, one reason why I was not bothered about my headphones not being balanced, I don't have ground loop issues on my setup, optical between DAC and source helps as well, yes. But on speaker cables it can be a big deal, because analog cables as I understand it from looking it up online, they act like an antenna, which is why lengthy RCA runs are not good, on top of the potential for ground loop issues, they do not have common mode rejection. 

[Pentium100 2,294]

45 minutes ago, Dawnshine Wonder said:

But on speaker cables it can be a big deal

For speaker cables it does not matter because the voltage is higher and speakers are low impedance.

45 minutes ago, Dawnshine Wonder said:

The added benefit of external DAC is XLR balanced which is excellent.

 I have a tape deck that has balanced inputs and outputs, it was kind-of annoying to connect to the rest of my system (which is unbalanced). Normally, yeah, balanced is better, though most of my stuff is unbalanced, so that's what I use. Ground loops are annoying and I sometimes have to use isolation transformers for the signals or disconnect some equipment from the ground to avoid them. Then again, my main PC has an internal sound card and I have a few other devices connected to the system. 

I sometimes think about getting an external DAC and ADC (the sound card has optical input ant output), it would help with the ground loops, but TOSLINK has max cable length of 10 meters IIRC. I would need a ~7m cable so it should be doable, but near the limit. Another way to do it would be to use sound over IP (something like Dante), but that equipment is expensive. 

Maybe I should buy a 10 meter TOSLINK cable and try connecting my PC to my DAT deck (which has optical inputs and outputs) to test if it is doable, then look for a DAC and ADC.

[Dawnshine Wonder 2,704]

Toslink does have its limits, but if we're using wired headphones we're sitting close to our audio gear, Toslink's cable length is not a problem for us. That is true, it is galvanically isolated, which is why I do wish the Spdif protocol got updated to support more modern formats like Dolby TrueHD, it didn't, so we're stuck with 2 channel lossless, again not a problem for headphones, but it is a limit for 5.1 setups as the signal has to be compressed to support 5.1. The problem isn't optical cabling, if it were, fiber optic would not be used for broadband which requires much higher bandwidth than audio does, yeah it may require more expensive types of fiber optic than what consumers would normally buy for their HiFi system, but I think in this case the benefits are worth it, and you don't have to rely on USB isolators to do the job which are often far more expensive than Toslink cables.

 

Paul at PS Audio was annoyed about the stagnation of Toslink technology as much as I was, it should have been updated, but for some reason, it wasn't. Instead we ended up getting inferior alternatives that relied on our gear not having shoddy circuitry in them. Thankfully my Schiit Magni Unity with DAC card is well isolated thanks to USB Unison, but not all DACs do that. Many other people assume based on ignorance that just because it's digital, USB cannot get interference, you know this which is why you had to disconnect some parts of your setup to prevent ground loop problems.