While going over Larvy's sampling theory white paper two statements in particular triggered my curiosity.

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What I take from this is that higher samplerates can create sampling inaccuracies. This is do to hardware limitations when running at these higher rates.

I wanted to test this in a real world situation for myself.

So with three different converters on three different DAW's, I performed a 11sec DA/AD loopback test at 48,96,& 192khz.
Avid/Digi 192 via protools
Lynx Aurora via protools
TC 24d via sonar

For analyzing purposes I used a 1khz square-wave. This keeps this test strictly in the audible realm & makes for easy visual comparison.

As far as I can tell the higher the samplerate, the higher the error/audio inaccuracies.

I find the results surprising & i'm interested in others thoughts on the matter.

FYI- do to protools less then stealer waveform detail, analysis is done via Sonar. If others would like to contribute to the test I've included the test files.
192khz square wave.wav
96khz square wave.wav
48khz square wave.wav

Test file info - These files have been generated from within protools via the signal generator @ each samplerate. No SRC.







The actual gain (volume) deviates pretty drastically @ 192. You can see how the deviation increases with increased samplerate. This is something you can see change on a peak meter.
There is as much as .3dbfs of fluctuation @ 192.

I admit i'm surprised to find this, I figured if this is case with most converters people would be more vocal.
For myself if this is correct the deviation @ 192 is unusable & still disturbing at 96.
This is with just a 1k tone, Imagine across the whole spectrum?
Hence this post. I'm trying to find an error in the test & would like some others try it on their systems. Would be nice to have files for comparison. Thoughts?

Unfortunately, your basis for testing is flawed...

1. A perfect 1kHz square wave is not at all completely within the audible realm. It has odd harmonic components stretching out way beyond audio frequencies. In the test files you generated the harmonics included are limited by the sampling rate; limited to fs/2. So in the 192kHz test there are harmonics as high as 91kHz; yet only up to 21kHz in the 48kHz test. The actual shape of the squarewave edges will also be highly dependent on the exact reconstruction filters used in the D/A, and those used in the A/D. This will be particularly noticeable in the amount of over-shoot and ringing. This also applies to how the files are viewed in editing software - does it use proper reconstruction (where again the exact filter will have an effect), or linear interpolation? So the peak values seen in the waveform view can vary drastically from converter, to converter, and possibly even software-to-software. (the 'flat' sections of the square wave should be the same - although analog gain inaccuracies play a part in this).
2. A visual comparison is not going to show you the accuracy differences I think Dan Lavry is talking about. Most likely these will show up as noise, which needs detailed analysis.

Also, for converters running at 192kHz (or even 98kHz), you cannot assume that they all behave similarly for inaudible frequencies (e.g. >23kHz).

Finally, I don't think you can test Dan's comments on accuracy and sampling rate but comparing any 'regular' converters (nor the same converter at different rates); there are too many other variables. You likely have to have 2 converters designed together from the ground up, with the same requirements (size, power, cost, etc.) and same architecture and parts as far as possible, except one is designed for some sample rate, and the other for a higher rate.

Thanks for the reply..

So are the level deviations being created from the AD/DA's handling of the extreme harmonic content?

Eric-
Your screen shots are basically at screen resolution, and therefore not very useful without the ability to "zoom" to the point(s) of interest. Can you make different screen shots with the waveform "zoomed" to a level where you can see the point of interest? It may also help to change the setting of the screen size to make a specific area larger before taking the screen shot (even if you cannot see the entire window).

You should also keep in mind that the graphic representation of the waveform as seen in an audio editing program may contain "artifacts" that are a result of the method used to generate the graphic display; and "aliasing" caused by factors such as how the pixel/screen resolution or size of the step drawn on the screen divides into the samples at any scale other than the level where you can see the individual samples will distort the graphical representation in a manner that has NOTHING to do with the accuracy of the actual encoding. Many waveform displays are not even accurate at the sample level; because even if you zoom to the sample level in the "time domain" (horizontal axis) it is necessary to also "approximate" the size of the steps in the "amplitude domain" (vertical axis) unless you are looking at extremely low-level signals. Remember, even with a 16 bit file here are over 64,000 "steps" in a full scale digital signal; so there is simply not enough pixels on any normal size monitor to represent this without some amount of approximation.

Many factors affect conversion accuracy. As Dan Lavry has pointed out many of these in his White Paper "Sampling Theory:"
http://www.lavryengineering.com/documen ... Theory.pdf

The loss in level at higher sample rates may be related to the the process of "sampling" the continuously changing analog waveform. But without seeing the design of the circuitry in question, it is hard to say exact what is causing this gain error. For example, gain error is not uncommon in analog filter circuits.

Brad Johnson
Lavry Engineering Technical Support

If you're talking about the 'level deviations' in your screen shots, as Brad points out... this could be due to the way the software is drawing the waveform on the screen. You need to look at the zoomed-in view showing individual cycles at high resolution. Even then, how it compares to actual analog signal is still dependant on how your software renders it on screen.

Also, the actual peak sample points in the recorded audio are likely quite different to the peak sample values in the original test waveform. There is likely to be 'overshoot' (compared to the raw sample values) in the analog (or properly interpolated) signal at the squarewave edges where a recording sample could be taken. This is the case even if the D/A and A/D processes are perfect (assuming that record and playback samples do not necessarily occur at exactly the same points in the waveform).

If I have time today I'll hook up our D-Scope for further analysis. (to be continued)