Compact Disc Sampling Rate of 44,100 Hz*

An Audio CD(Compact Disc) has a Sampling Rate of 44,100 Hz.

What does this mean EXACTLY?

I know it samples the analogue wave form 44,100 times per second, but what does this mean with regards to the frequency of what it is sampling?

I thought it was cut & dry and didn't matter what the actual frequency of the sampled wave was, but then I found this site:

http://www.saecollege.de/reference_material/pages/Recorders.htm

And it is saying that a 100 Hz signal only gets sampled 441 times per second, a 1,000 Hz signal only gets 44.1 samples per second, and a 10,000 Hz signal would only get sampled 4.41 times per second.

Now obviously they're just taking 44,100 and dividing it by the frequency of the signal being sampled, but is this right, or not!?

I am confused now!

 

From the web page:

WTF?

 

Obviously this person has never heard an old CD mastering or any of Steve's work. Besides, what exactly in the way of equipment was he using? As any audiophile knows some equipment has inherent frequency coloration so until we know all the facts this is a ridiculous statement other than it's theory IMO.

 

Hi gmrulz4u,

While I wouldn't necessarily agree with the conclusions reached as to this being "why digital high frequencies sound harsh" (or even that digital high frequencies *are* necessarily "harsh"), the explantion of high frequencies being stored in fewer samples is correct. That is to say, the "faster" signals won't get sampled as frequently as "slower" ones given a fixed sampling rate.

This is similar to a film camera "dividing" the continuous motion of life into 24 frames per second. Objects moving across the field of view at higher speeds will not be rendered as "frequently", read "clearly", as slower moving objects.

On an absolute level, yes, higher sampling rates can sound more natural. On a practical level, there would appear to be many factors that contribute to determining how the final record will sound. Analog records, after all, have an effective "sampling rate" of infinity, yet I've heard many that will loosen one's dental fillings. Bad microphone techniques, recording techniques, mixing techniques and mastering techniques can all make for "harsh" records, whether the medium is analog, 44.1 or high sampled digital. Conversely, I've heard some very, very good sounding recordings in each of these media.

Barry
www.barrydiamentaudio.com
www.soundkeeperrecordings.com

 

OK so is this right or wrong??? I am still confused...

Is the answer to:

Higher frequencies get sampled less often per second on a standard Audio CD?

YES or NO??

 

WRONG. The sampling rate is constant. 44.1 kHz means 44,100 samples per second. That what a Hertz is--a 1/sec.

I think what the author is trying to explain--perhaps not as precisely as he could--is that at 44.1 kHz, the *resolution* of the higher frequency signals is not as high as the lower frequency signals. Simply because of the wavelength of a lower frequency sound, that lower frequency sound will be spread across more samples. A higher frequency sound, with a shorter wavelength, will be spread across less samples. However, the redbook spec of 44.1 kHz is *double* the wavelength of the upper limit of human hearing (20 kHz) plus a "safety margin." I am not sure if I agree with the author's conclusions because this "safety margin" of 4,100 samples per second is built into the redbook spec to assure that the upper limit 20 kHz signal can be accurately resolved. Otherwise, the redbook spec would have specified a 40kHz sample rate to get to 20 kHz--the 40kHz sampling rate would be the absolute lowest sample rate that could be used to resolve 20 kHz, because the sample has to contain a crest-to-vallet-to-crest snapshot of the wavelength.

See this page here for a really easy to understand explanation of Nyquist sampling theorem:

http://www.cs.cf.ac.uk/Dave/Multimedia/node149.html

 

PHP:

it's a false bright created by the high frequencies sounding like square waves!! 

That's far more articulate than my everyday "sounds like crap" quote.

PHP:

Obviously this person has never heard an old CD mastering or any of Steve's work.

I have, and his re-mastering work on vinyl kills the CD everytime, at least that's what happens on my system.
And yes I'm talking about using the same title for comparison.

 

Thanks Eric,

I think you put it more clearly than I did.
Sampling rate is constant and that means higher frequency signals end up being caught at a lower resolution as a result.

Barry
www.barrydiamentaudio.com
www.soundkeeperrecordings.com

 

That's far more articulate than my everyday "sounds like crap" quote.

I have, and his re-mastering work on vinyl kills the CD everytime, at least that's what happens on my system. And yes I'm talking about using the same title for comparison.

 

Not less often per second, but less often per wavelength .......which results in lower resolution at higher frequencies.

My question relating to this problem is: how many samples are necessary to not hear the digitality of the signal?

In the movie film example speeding up the frame rate solves the resolution problem with fast moving subjects and we do some of that with DVD audio, right? Is the 1000Hz sampling (44.1 per wavelength) adequate to fool our hearing or do we need more resolution, still?
Surely someone in the beginning has tested this and concluded that certain compromises were good enough for the average listener. Are these test results published out there somewhere? Are we listening to media with a bandwidth of 20Hz-3KHz, for instance and everything above that is noise?

 

Barry,

Unfortunately I edited my post to add information and now it is probably more confusing thatn anything else written in this thread!

Your explanation is good. I am not an audio engineer by any means, but I have studied physics and read a few white papers on digital audio sampling theory, so I think I'm *reasonably* informed for a layman . . .

 

Hi Flatlander,

According to Nyquist, upon who's theorem our current digital audio standards are based, two samples are required to re-construct the original waveform.

Will it no longer sound "digital"? I think that depends on the recording. I've heard too many analog recordings that sound too "digital" as well.

As Yogi Berra said: "In theory there is no difference between theory and practice. In practice there is." ;-}

Barry
www.barrydiamentaudio.com
www.soundkeeperrecordings.com

 

I could probably believe that, in theory, except that no two instruments produce the same wave form. Sure all flutes are similar on a 'scope and saxophones resemble clarinets, but something with a percussive attack tends to get lost. Even something like chimes are not reproduced faithfully, by taking samples every so often.
What if a restaurant served us a digitally sampled meal ... every few bites there was something included that was not a good byte in the entree, but it resembled the original ... plus or minus a standardized tolerance ...

I think Mr. Berra was right on target with that comment.

Don't get me wrong! I'm not against digital, but I believe it can be improved, today.

 

I think the usual argument in favor of the adequacy of a 44.1 KHz sampling rate is that it allows the original signal to be reconstructed faithfully to the accuracy needed by the frequency limits of human hearing, which at the very best goes as high as 20KHz. The argument is over whether there are aspects other than pure-tone (pitch) frequency response that come into play with human hearing. Certain kinds of distortion are also introduced by the digitizing process, such as higher-order harmonics for example, which sound harsher than the 2nd-order harmonic distortions specified in the industry standard conventional audio measurements of equipment (the THD spec.). The question is whether these higher-order distortion components are sufficiently strong as to be audible. Many people think they are.

Also, in order to reconstruct the analog waveform for output from a CD player, filters are used to smooth the response. It is thought by some designers that it would be easier to design good-sounding filter circuits if the sampling rate were higher and the filters could be less steep in their slope of frequency response (rolloff rate). The steep filters can produce another kind of distortion which may be audible (ringing). I believe this may be the basis for the upsampling - artificially doubling or quadrupling the clock rate of the digital signal within the player of redbook CD playback in some players before the filter stage. I could be misinformed about that; I've never really studied this issue.

 

Hi Flatlander,

Please don't get *me* wrong. I agree with you 100%.

Barry
www.barrydiamentaudio.com
www.soundkeeperrecordings.com

 

I have never seen it explained in quite that way, or that way at all. That's why my reaction to that passage of the the article. Actually, it sounded more like an explaination of perceptual coding.

 

So digital artifacts would be like wheels rolling backwards in film and video...

 

Folks, There have been other threads on this subject in this forum and even in the music forum. I has been fiercely debated as to the importance of sampling frequency as to how it effects the sound. People with strong scientific and mathematical backgrounds have disagreed as to what is important. I have a Ph.D. in physics, an under graduate minor in mathematics, have written a paper on some of the aspects of digital theory and practice and 25 years ago designed and built an industrial grade digitizing system for audio frequencies. Clearly I understand how digital systems work, however, for this forum what is important is how they sound. As I said above people who are digital "expert" disagree as to what is important. So unless you have a strong math and science background I would not worry about articles like the one that started this thread and let your ears decide what sounds best.

 

The above quoted paragraph is wrong in so many ways, I don't even know where to begin.

Sampling at 44.1 KHz means that 44,100 samples are taken per second. The Nyquist theorem guarantees that each frequency below 22.05 KHz is reproduced. The limited bitlength of the samples (i.e. 16 bits) introduces certain rounding errors, but these are related to the volume and the dynamic range, not to the frequency.

A 20 KHz wave, sampled at 44.1 KHz, will not result in a square wave after the digital/analog transformation, not even a piecewise straight curve.

Sampling is not choosing points and linearly connecting the dots. It is far more complex, and the Fourier analysis behind it will always produce sums of sine curves.

 

Tony, was your paper published, or would you consider sharing it or making it available to forum members? I'd be interested in reading it.

 

Harold, No the paper was not published, it was my senior project in math that I had to do to get my math minor. It was on Chebyshev polynomials and series and how when you use them to approximate a square wave you get ringing as you do when you use any finite polynomial sequence to approximate a square wave, however, in the case of Chebyshev polynomials there is no "over shoot" as there is with other polynomials. Since this was for a math professor it was not written for layman consumption and was 90% equations. Here is a link on Chebyshev polynomials that will give you some idea of what I mean by almost all equations.

http://en.wikipedia.org/wiki/Chebyshev_polynomials

 

Thanks, Tony. I remember Chebyshev filters from Electrical Engineering courses, and even designing some circuits, but we didn't get that heavily into the math. We derived a kind of cookbook-type of formula to use to produce desired system responses in feedback-control circuits instead of working with the polynomials. The idea of course was to avoid ringing and overshoot when you were controlling motors to set positions and distance of mechanical movement/rotation and things like that. The same thing would apply to response in audio filter circuits. Not for the layman, as you say! After all these years I'm afraid I'm back in the layman category.

 

This makes sense to me and I think they are audible. Everything or anything involved is going to provide for some amount of distortion (color). Do the higher resolution formats reduce the distortion you mentioned or just sample faster and introduce their own inherent distortion?

 

I don't really know for sure. It may push the higher order harmonics up in higher in frequency where they are inaudible and/or more more easily filtered out of the signal in the player output circuits. I must confess I haven't read much technically on the newer high-res formats.