Dirty Digital Delusions
This page was written to critically assess some of the claims made in a magazine article that appeared on pages 22 and 23 of the July 2008 issue of ‘Hi Fi World’ (HFW) magazine. Alas, as the following indicates, much of what appeared in that article was either incorrect or misleading...
The basic assertion of the article, which was titled “Dirty Digital”, was that CD Audio unavoidably suffers from high levels of distortion at low signal levels. Unfortunately, the article gave misleading results. The reality is that correctly made recordings will employ dither, and this will remove the ‘problems’ described in the magazine article.
If you want to know more about dither, then click here. On this page I will simply concentrate on the assertions made in the HFW article and examine the ‘evidence’ offered in that article.
At the top left corner of page 23 of the magazine article a spectrum is shown. It is accompanied by a claim that: “A 1kHz tone at -60dB and 1002Hz produces 1% distortion, this analysis shows...”
The spectrum in the article does show a series of ‘spikes’ that look like distortion products. However the one above shows a very different result. This spectrum (as with all the others I present on this page) was obtained from CD Audio format data – i.e. 16 bit integer values sampled at a rate of 44,100 samples/sec. The FFTs were done using 32,768 samples. If you examine the above you can see a 1002Hz sinusoid at the -60dB level. But there are no signs of the quantisation distortion spikes that appear in the article. Indeed, there are no signs of any such spikes above the noise floor. The distortion level is unobservable and must be well below the 1% value claimed in the magazine article. (I used 1002 Hz here as this seems to be the frequency used in the article, but the magazine claim is ambiguous on this point. In fact also tried 1000 Hz and got results which also showed no signs of distortion.)
The main reason for the discrepancy seems to be that the author of the magazine article did not dither the sequence of sampled values which he then used as the ‘test tone’ for his measurement. Unfortunately, this means his test tone wasn’t actually a sinusoid. Failure to dither means the waveform will have essentially been ‘pre distorted’ when created or recorded. The CD player might then have faithfully reproduced this non-sinusoid. But since what was recorded wasn’t a sinusoid it didn’t output a tone without any other spikes in the spectrum. One of the basic precepts of digital sampling – and indeed more generally of measurement theory – is that sets of values like this which are to define a pattern may have to be dithered. It is therefore a standard in digital audio to dither. As the above spectrum shows, when you do this, the result emerges without the claimed 1% distortion. The result also demonstrates that it is incorrect to presume that it is inevitable that a low level signal must be distorted by the claimed amount by CD Audio recording and replay. Do the recording correctly and the claimed problem simply need not arise.
At the bottom right of page 23 another spectrum is shown in the magazine article. Here the claim made is that: “A tone at 9130Hz produces strong quantisation products...” The spectrum in the article does, indeed, seem to show a forest of distortion spikes.
As before, however, if we correctly employed dither when the test waveform was created/recorded the quantisation distortion evaporates, as illustrated in the above spectrum. Again, all that is necessary is that the person making the recording should understand that dither will have this desirable effect.
In both the above cases about the most we can say about any ‘inherent’ distortion is that – when correctly recorded into CD Audio form – the distortion must be well below 0·1%. Not the 1% or so alleged in the magazine article. Indeed, no real signs of distortion appear in the above spectra. The dither applied in each case produces a broadband background noise level of about -92dBFS.
Curiously, the article also shows a spectrum at the bottom left of page 23 and makes the assertion: “A tone at 8820Hz produces no quantisation distortion products...” Yet if you look carefully at the spectrum printed in the magazine beside this statement you can see that it displays a component somewhere between 14 and 20 kHz as well as the 8820 Hz test tone! The reason for this is that the higher frequency component that the magazine text ignores may well be a quantisation artefact. But it appears at a nominal harmonic of 8820 Hz because of the simple 1:5 integer relationship of 8820 Hz and the sampling rate of 44100 Hz. The following spectra may cast some light on this.
The above shows the spectrum of an undithered 8820 Hz tone. As with the spectrum in the magazine article another component appears at about double 8820 Hz.
The above shows the spectrum of a correctly dithered 8820 Hz test tone. The component at double the test tone frequency has now vanished. I can only speculate at this point, but the comment in the article is consistent with the author assuming the component (caused by lack of dithering) was present for some other unstated reason. Hence he presumed it had nothing to do with quantisation distortion manifesting as a consequence of his not dithering the test tone he employed.
The reason the 2 x 8820Hz tone appears when the test tone was undithered is the 1:5 ratio between the test tone and sampling frequency. In the absence of added dither each cycle of the 8820Hz will consist of the same 5 values, and this sequence will repeat precisely during each cycle. The result is that any distortion products generated by the failure to dither the signal will occur at simple harmonic ratios of 8820Hz. Thus the result may look like conventional harmonic distortion when viewed, but is actually due to quantisation effects as a consequence of the failure to dither when creating the sequence of CD Audio sample values. Dithering removes the problem.
The magazine article displays a graphic on page 22 that claims to show the distortion percentage at various signal levels. Alas, this graphic is rather misleading.
Signal Level
(dBFS)
|
Magazine
Claim (%)
|
H5 (%)
|
H10 (%)
|
| -90.00
|
|
0.98121
|
1.38763
|
| -80.00
|
10.0
|
0.31028
|
0.43881
|
| -70.00
|
|
0.09812
|
0.13876
|
| -60.00
|
1.7
|
0.03103
|
0.04388
|
| -50.00
|
|
0.00981
|
0.01388
|
| -40.00
|
|
0.00310
|
0.00439
|
| -30.00
|
0.04
|
0.00098
|
0.00139
|
| -20.00
|
|
0.00031
|
0.00044
|
| -10.00
|
|
0.00010
|
0.00014
|
| 0.00
|
0.001
|
0.00003
|
0.00004
|
The table above shows the measured distortion levels for correctly dithered sinusoids using a waveform extended over 32,768 CD Audio sample points. For comparison, the values claimed in the magazine graphic are also listed in red-coloured text. The harmonic spot frequency method was used to obtain the nominal distortion results from the 32k spectra. H5 uses the harmonics up to 5x the test tone frequency and H10 up to 10x. Slightly larger values would have been produced by using more harmonics.
Looking at the spectra used as examples on this page you can see that in general there is no sign at all of any distortion when the test signal waveform was correctly dithered. As a consequence the H5, and H10 values show no sign of being due to actual distortion. The values are essentially due to noise, and any actual distortion may be well below the values quoted above. The power at the spot harmonics used for H5 and H10 seem just to be the portion of the wideband noise that falls at the harmonics. If a longer duration than 32,768 CD Audio samples had been used, lower H5 and H10 ‘distortion’ values could have been obtained from the same test waveforms. From the results on this webpage it should be clear that there is actually no sign of any distortion at the levels claimed in the article.
If you examine test reports on CD Players in magazines other than HFW it is routine for them to show measured distortion levels broadly similar to the H5 or H10 values listed in the table The values obtained will vary to some extent, depending on factors like how many harmonics were summed to obtain a value, and duration of measurement. But results for excellent CD players tend to be consistent with the values shown above – and are often orders of magnitude lower than the claimed values I have listed in red text!
Under the magazine graphic, the article contains the claim: “Dynamic range is limited to 85dB or so by dither noise...” In fact this assertion is either misleading or incorrect. It would certainly be possible to employ an excessively large level of dither/noise and get such a result. Also, it may well be the case that real-world sound recordings – particular ones taken from analogue sources like old master tapes – have that much noise. However optimal triangular probability distribution dither would allow the noise level to be below -90dBFS, probably more like -92dBFS. So there is no need to presume that all CD Audio recordings must be limited to the range claimed in the article.
The magazine article does briefly touch upon the use of dither. But the wording could easily lead the reader into thinking it is only relevant for signal levels of around -80dBFS. Such an assumption would be incorrect. As shown by the above examples, correctly applied dither has the beneficial effect of completely suppressing the quantisation effects shown in the magazine article, and will do so for any signal level or in-band frequency. This has been well known for some decades. The first articles explaining this for audio engineers appeared some decades ago, and by now it should be routine practice to employ dither to ensure the distortions that feature in the article simply don’t arise with correctly made recordings. The conclusion is therefore that many of the statements and values presented in the HFW article should be regarded as either inaccurate, incorrect, or misleading. The author of the HFW article claims that CD Audio, “...suffers from hard grey sound.” I can’t speculate on why he thinks this. I can only note that his article does not seem to provide any basis for the assertion which stand up to scrutiny.
Of course, the above is no guarantee that a specific CD player or disc won't have high levels of distortion due to some particular problems with that player or disc. But this does not mean the general results for the CD Audio format are anything like what was claimed in the magazine article! Indeed, as pointed out above, if you examine the results published in various places you should be able to find that many players have been measured and found in practice to have lower distortion levels than claimed in the magazine article.
