OT - Sample Rate Question (Nyquist???)

TielBr wrote on 8/29/2005, 8:52 PM
Ok,… Off-topic perhaps, but I have a general question for anyone that might know…

As far as sample rates go, why the need for anything beyond 44 KHz? I may be totally off track here, but I do have a background in electronics, work for a major cellular company, and am still lost.

Most of my knowledge here is in wave propagation, and it is entirely possible that in the digital storage realm, I’m a mental midget. BUT there is a thing called the Nyquist Frequency. With this in mind, when transmitting information, you must have a carrier frequency that is double that of the information that you wish to transmit. In the audio realm, the highest possible recorded frequency is debated to be between 20KHx – 22KHz. That would make the Nyquist Frequency about 44Khz. I imagine that would be the reason that the Red Book standard sample rate for audio CD’s is 44.1 KHz, just over the Theoretical Nyquist Frequency, possibly allowing for some headroom.

If that is the case, then why all the craze about 96+Khz Sample rates, and when I listen to an MP3 with a sample rate anywhere below 128K, the cymbals and other higher frequency instruments sound all funky to me.

I get the fact that different compression techniques will yield different results, but if it’s over 44 KHz, than why can we hear the difference.

I’m really interested to know what’s up with this, so if anyone knows the answer, or can theorize what’s up, please let me know.



bgc wrote on 8/29/2005, 11:04 PM
Yup, the scientific and artistic merits of higher sample rates is a long area of debate.

You are right that Nyquist comes into play which says that for a given sample frequency you can perfectly reconstruct digital signals with frequencies up to half Nyquist.

However, I think you are a little confused after this point when you say the "highest possible recorded frequency" is around 20-22kHz.
What is actually true is that most people can't HEAR above 20kHz or so and so people argue that you don't need to record above those frequencies. In fact some people can hear well over 20kHz and so this is an average limitation. There are several factors that make recording at higher sample rates of interest.

For one, all digital recording systems have to worry about aliasing and therefore the audio needs to be filtered to "kill" all frequencies above Nyquist. If your sample rate is low enough to be near the 20kHz hearing limit, then these filters have to be "brick walls" and work very hard. This can cause audible artifacts in frequencies that you can hear. The higher the sample rate, the less hard the filters may have to work.

There are also lots of non-linearities in our ears and hearing system. In fact frequencies higher than 20kHz can interact and create audible audio at lower frequencies. Bizaare but true and some people think this might have something to do with why people like higher sample rates.

There's also the issue that not everything we experience with audio is actually "heard". We also perceive audio by bone conduction (bass) and through our skin and this may be part of it too.

It's a wide area of debate and can verge on a "religious debate". Given that, I suggest you record at whatever your hardware can handle and what you can appreciate.

Regarding MP3, I think you're confusing sample rate with data rate. MP3 at 128k is actually stereo audio being encoded at 128 kilo bits per second. This is usually encoding of 44.1 kHz sampled audio. MP3 is a lossy data reduction scheme that uses psychoacoustics to dramatically reduced data rate (i.e. getting about 10 to one compression of PCM audio by throwing away portions of the audio you don't hear based on frequency masking).

When you encode MP3 below 128kbps, one way to reduce the bit rate requirements is to reduce the bandwidth of the audio (MP3 is actually limited to about 16kHz I think). As the rate goes down, so does the bandwidth as the data rate is essentially tied to how many frequency bins you're trying to encode (this is a gross simplification but helps some).

I've worked a lot on the Dolby Digital and Dolby E audio coding systems here in San Francisco, so have spent some time in this area :)

Since I've covered several topics which normally are dealt with over months of classes there ARE A LOT of things I've glossed over + I'm tired (and I'm sure others will point out) but it's enough to get some good Google sessions going :)

Have fun!
Chienworks wrote on 8/30/2005, 10:16 AM
That frequencies can be accurately reproduced up to 1/2 the sampling rate is a myth. The waveform can be approximated, but not accurately reproduced. As you approach the higher limit there will be aliasing effects. At higher frequencies there aren't enough data points to represent the full wave. The samples may come at "non-representative" points in the wave form and the result will be a radically different shape. Simple sine waves near the nyquist frequency end up being more like triangle waves and will sound harsher. While the frequency itself may be reproduced, what the sound sounds like can be drastically altered. Using a higher sampling rate allows more accurate representation of the waveform at higher frequencies.

128K is not the sample rate for the MP3 file you refer to. That is the data rate, as in 128kilobits per second are used to store the data. It is sampled at 22050 or 44100Hz.
bgc wrote on 8/30/2005, 2:19 PM
If you apply Nyquist's theory mathematically you get perfect reconstruction of digital signals.
Of course, as you point out, aliasing and the steps needed to remove it (filtering) makes this un-true in practical/real-world applications.
mpd wrote on 8/30/2005, 5:29 PM
Mathematically, the sampling theorem is not a myth. Practically, it is. It is not that there are not enough points to reproduce the waveform, it is due to non-ideal filter implementation.

Brickwall filters (both analog and digital) are unrealizable. Actual filters have transition bands. In an A/D, the transition band decreases the usable bandwidth, and you can't have total stopband rejection, so there is some aliasing. I am pretty unfamiliar with current A/D designs used in audio gear, but when I worked in digital communications we used 80% as a good rule of thumb for the usable bandwidth. On the D/A side, you have similar problems with the transition band, but instead of aliasing you have imaging.

One place where higher sampling rates helps is with digital implementation of dynamics. Compression and expansion are non-linear effects, and as a result can cause frequency splatter. With lower sampling rates, this splatter can alias, where with higher sampling rates, the power of the aliases is much lower, so it is less noticable.
LarryP wrote on 8/30/2005, 5:42 PM
Like bgc alludes to Bob Katz, in his Mastering Audio book, makes a good case that what we really are hearing is the ripple caused by the 22.khz. brick wall filter. Higher sampling rates allow that filter to be moved to a frequency well beyond our hearing.

Based on the experiments he described with 0.5db of ripple this is the most plausible explanation that I’ve heard so far of why higher sampling rates sound better (“more open”, “better imaging, etc.).

bgc wrote on 8/30/2005, 7:36 PM
This is also why the UA Pultec EQ is upsampled internally to 192kHz (to reduce distortion in the model).
That's actually one of the "big deals" about the Line6 amp modelling is that they internally upsample the audio (something like 8x) so that all that distortion that they create in the digital domain doesn't alias back around and sound like cr*p.
I'm actually much more of a nut about bit depth :)
TielBr wrote on 8/30/2005, 8:34 PM
Thanks to all for the replies. I'm the type of person that doesn't know it all,... but really wants to,... and theis was REALLY bothering me. I have a lot to go on now, so I can learn away.
Thanks again,
John_Cline wrote on 8/31/2005, 8:39 PM
In order to recover all Fourier components of a waveform, it is necessary to sample more than twice as fast as the highest waveform frequency. So, if 44,100 samples per second is the sampling rate, the Nyquist frequency, also called the Nyquist limit, is the highest frequency that can be coded at a given sampling rate in order to be able to fully reconstruct the signal.

Just to be clear; the Nyquist frequency is not 44.1khz, it is 1/2 the sample rate, or 22.050khz.