More than we hear (with a CD player)

[NTTY]

Hello Everyone,

Several of you are regularly asking me what are the measurements of importance and how to perform them, when it comes to review a CD Player. This post tries to reply to these questions.

Introduction​

As some of you know, I'm a lot into the good old silver disc and I like to review old or new CD Players (eg the Sony CDP-337ESD or the Denon DCD-900NE). For the last couple of years, I experimented a lot of measurements and ways to achieve them, using external sources, references, replicating what others did before me and comparing my results. For instance, Amir wrote an AES paper about the measurements he performs on high resolution DACs, or John Atkinson wrote a long article "As we see it".

The below explains the measurements I perform to date, when reviewing a CD Player. It all started with the need to create a reference test CD, as the CD Player itself is used at the generator of the test tones in this case. The below addresses how this test CD is put into action when it comes to report measurements and their purposes.

Most, but not all of the below applies to digital and analog outputs, although they make real sense with analog outputs when it comes to a CD Player. Some of you like to know how a CD player behaves when used as a Transport. I will mention when the measurements do not apply or apply partially.

THD, THD+N, SINAD, ENOB and SNR​

Be good at the basics

These are the most known, understood and published data. I report them via an FFT analysis of a pseudo 1kHz sine tone.

For this standard and regular test, I slightly deviate from the pure standard dithered 1kHz, or the 997Hz which the AES17-2020 recommends, for the below reasons:

• Tests tones of 1khz or 997Hz have been in use for decades. The 997Hz became largely used because it is a prime number and so has a sub-frame pattern less repetitive with 16bits data, which means it less disrupts the FFT view when analyzing correlated distortion content.
• To prevent sub-pattern to come in the analysis which is intrinsic to the PCM 16bits/44.1kHz format, and as recommended by the AES, we can use dither. This is a low level "random" noise that has the property to reduce the quantization errors of the conversion to digital. Thus it removes the sub-frame pattern at the expense of an increased noise floor.
• Dither adds low level noise, some more than others (rectangular or triangular). With the CD Player, we can clearly see the impact of that noise, as opposed to high bit depth DACs (24bits). This has proven to prevent analysis of elevated level noise floor that some CD Players suffer from, especially when playing a full scale tones.
• I went with 999.91Hz test tone for that reason. This tone has the property to "self dither", and that means it has a repetitive sub-range every 14secondes only (thanks @danadam for the code) which is more than enough to perform a 32 averages FFT.

The result is shown in Figure 1, that is anFFT of the 999.91Hz test tone at 0dBFS (which is the digital maximum output):

Fig.1 : Sine tone 999.91Hz @0dBFS without dither, from a CD player​

The dashboard shown in Figure 1 displays a lot of information, and not all analysis software will show the same:

• Test tone: You can see first that the test tone is captured at exactly 999.91Hz, which means a clock that is below 10ppm and that is very good. A 999.88Hz, for instance, would be a -0.003% deviation, or -30ppm (that would still be considered good).
• THD: The Total Harmonic Distortion is made of the sum of all harmonics of the test tone (its multiples), they are the generally the highest spikes you see beyond the test tone. If the case of a CD Player, and even if the max resolution is the theoretical -96dB, we could still hear a -100dB tone into noise. So, as usual, the lower, the better.
• THD+N: In many cases, the THD+Noise will be dominated by the noise, as we can see in the above example. That's why it's interesting to understand the difference between noise and distortion.
• SINAD: The SIgnal-to-Noise-And-Distortion is deviated from the THD+N and is its opposite expressed in dB. So that is 94.7dB in the above example. SINAD can be calculated at various digital levels (below 0dBFS), of course, but is often given at full scale only.
• ENOB: The Equivalent Number Of Bits is deviated from the SINAD by the formula ENOB = (SINAD - 1.76dB) / 6.02. In reality the full formula accounts for a potential additional headroom since it is deviated from the SINAD which can be performed at lower levels. Please read this tutorial from Analog Devices, should you wish to know more.
• SNR: The Signal to Noise Ratio, with the CD Player and 16bits data, has a maximum value of SNR = 6.02N + 1.76dB (where N=16). So that is 98.08dB. I report SNR values as per the dashboard, that means always in the presence of signal, since some DACs shut themselves down without signal, artificially increasing the SNR value. I verify if the calculated SNR is the same with 0dBFS and -20dBFS data and reports if the difference is above 1dB.

I also like to show the same dashboard, but with a -6dBFS test tone as it often draws a different picture. Indeed, the 0dBFS test is considered "extreme" by some, likely to generate a beginning of ASRC/interpolator/DAC saturation which I think is bad. So a view at -6dBFS can tell us more about that. Here is an example with the same player as above:

Fig.2 : Sine tone 999.91Hz @-6dBFS without dither, from a CD player​

As you can see:

• The SNR has decreased by an exact 6dB, since we play 6dB quieter and so the signal is lower, say closer to the noise floor, hence the reduction.
• THD also decreased by roughly 6dB which means that the CD Player had no issue at playing a full scale test tone.

dBFS, dBr, dBc and distortion in % vs dB

In Audio, we expressed very often everything in dB. You see in my graphs that they are in dBr, which is kind of a standard way to represent a signal relative to its maximum (that is the r, for relative, in dBr). We could also represent in dBFS, which in this case is no longer relative to the signal being played, but to the full scale digital signal (dBFS = dB Full Scale). The big difference is that the noise floor seems visibly higher (in dBr) but it hasn’t changed.

This is an example below with a test tone played at -20dBFS, and represented with a dbr scale:

Fig.3 : Sine tone 999.91Hz @-20dBFS without dither, from a CD player, vertical scale in dBr​

Now the same signal in dBFS:

Fig.4 : Sine tone 999.91Hz @-20dBFS without dither, from a CD player, vertical scale in dBFS​

Nothing has changed except dBr to dBFS and that can give the impression the noise floor has decreased, but it's not the case. THD, THD+N and SNR are still calculated relative to the signal, as this is their mathematical definition.

Of course, with a signal at 0dBFS, you get the same view in dBFS or dBr since we are at the maximum digital output. Note that dBc is the same concept as dBr where we represent and measure relatively to the carrier (c) which is useful when we don't have the reference to the full scale.

And special note about that ancient way to talk about distortion in percentage instead of dB. I personnaly do not like it and so I use only dB. There are online calculators to help you if you need, like this one. The relation between the linear % scale and the logarithmic one in db is as below:

• THD of 1% = -40dB
• THD of 0.1% = -60dB
• THD of 0.01% = -80dB
• THD of 0.001% = -100dB
• THD of 0.0001% = -120dB

If the SNR and noise is limited by the CD Audio format, the internal (or external) DACs can achieve THD below -98dB, exemple with this one:

Fig.5 : Sine tone 999.91Hz @-20dBFS without dither, from a CD player, vertical scale in dBFS
​

You can see a THD of -113.7dB, which is excellent and what is achieved by modern DACs. And with that, time has come to talk about the FFT gain.


FFT Gain - It's a kind of magic

Per Figure 5 above, you might get the feeling that the noise floor is way below the calculated -100dB (you see it at around -140dBr on the graph). It's only an impression and a mathematical effect of what we call the FFT gain. Indeed, the property of the Fast Fourier Transform is to highlight the frequency components of a signal (it is a frequency decomposition of a signal). An FTT as we perform them can be seen as large number of super narrow pass-band filters run at the same time. They filter everything around their focus of interest and all together have the effect of lowering random noise.

The FFT gain depends on its "length" which determines the number of super narrow pass-band filters which we call FFT bins.
It can be calculated as FFTgain = 10 * log(FFTlength / 2). With an FFT length of 256k, it means the FFTgain = -51dB. And so the random noise visually decreases by that value, hence revealing the periodic components of the signal, below the random noise.

As a personal rule, I use an FFT length of at least twice that of the sampling rate input of the measurement interface:

• If I use 44.1kHz at the input, FFT length is 128k
• f I use 96kHz at the input, FTT length is 256k
• If I use 192kHz at the input, FFT length is 512k

These ensure that I see the virtual noise floor roughly in the same place, so I don't get negatively or positively surprised looking at the graph.

Figure 5 was a measurement performed at 96kHz input (it allows wider band analysis) with an FFT length of 256k. That means the random noise was lowered by that much (-51dB).


That's not all about the pseudo 1kHz FFT view

It is sometimes interesting to look at the same test tone, but with a wider band view. My standard measurements go to 48kHz, but sometime I go up to 96khz when it's relevant, as shown in Figure 6 below:

Fig.6 : Sine tone 999.91Hz @0dBFS without dither, from a DAC (24bits)​

The reason to go that far is to show other elements than only harmonic or intermodulation distortion and correlated noise. In this example, we can the noise shaping technique of the DAC showing its effect beyond 50kHz.


And at lower levels?

The analysis of the pseudo 1kHz can be done at any digital level and it also reveals a lot about a DAC's behaviour at lower scale. The below Figure 7 is an example of two DACs with the same 999.91Hz test tone, without dither, but at @-20dBFS.

Fig.7 : Overlay of a sine tone 999.91Hz @-20dBFS without dither, from R2R and 1bit DAC.​

The ancient R2R DAC, of 1990, shows more distorsion than the modern 1bit. You can see 30db more on the Second Harmonique, where the plot is on the graph, and as displayed in the legend).
At lower scale, with CD Players, the distorsion should be buried into the noise floor. But it was not the case some decades ago, and it could still be the case with not so well implemented modern DACs too. So that is an interesting analysis too.

I personally run the same measurement at 0dBFS, -1dBFS, -3dBFS, -6dBFS, -9dBFS, -12dBFS, -16dBFS, -20dBFS, -39.99dBFS, -49.99dBFS, -59.94dBFS, -70.31dBFS, -80.77dBFS and -90.31dBFS, all without dither.

For example, Figure 8 shows the two same players as above, but at -70.31dBFS:

Fig.8 : Overlay of a sine tone 999.91Hz @-20dBFS without dither, from R2R and 1bit DAC.​

Again the noise floor is higher because the view is in dB Relative, as I explained before. The signal is much lower, to a point that a recorder would consider this is silent, by the way.
Figure 7 shows that, at this very low level, the quantization errors have very much increased, which is normal. Indeed, we now have only so few bits to represent the signal, and so the rounding errors when computing the sine wave increase, generating more distorsion and noise, as you can see. And you can also see that one of them have more distortion than the other.

Of course, this is without dither or noise shaping technique which I will address later.


What about digital output?

The pseudo 1khz can be analyzed in digital, up to the limit of the sampling rate, which is 22.05kHz, as there is nothing digitally recorded on the CD Audio beyond that.
I extended the below view to 30kHz on purpose:

Fig.9 : 999.91Hz @0dBFS (without dither) from digital output of a CD Player​

You can see that there's no distortion, as there isn't on the test CD, and the limit of calculated THD is limited by the small quantity of quantization noise due to the representation in 16bits of the test tone. This is what the output of a CD Player should show, and most achieve that. Some would show a higher noise floor, or lower that full scale (you see here -0.00dBFS reported by the software) and sometimes distortion components, all of which would mean transformation of the digital signal.

Dynamic Range​

As per the AES17-2020, the Dynamic range is the ratio of the full-scale level at the output of the CD Player to the weighted noise and distortion level in the presence of low-level signal.
Per the AES, the test signal shall be 997Hz, but I deviate again with 999.91Hz, not that it changes this measurement. The test signal shall be @-60dBFS.

The measurement method implies to set the interface so the maximum output of the CD player (a sine tone played at 0dBFS) is shown at 0dBFS at the input of the interface (by its ADC). Per my own convention, I keep around 1dBFS margin at the interface input to prevent clipping it. So I need to account for that when manually calculating the DR.
Then I play a -60dBFS test tone from the CD Player and read the N+D (A weighted) value minus the headroom I kept at full scale.

Here is an example with Figure 10 that is a -60dBFS measurement from one of the first a CD Players (1982) which had only 14bits resolution in its DAC section (but was using an oversampling filter of 4x with Noise Shaping to compensate for the missing two bits) :

Fig.10 : 999.91Hz @-60dBFS, 14bits CD Player (1982)​

DR is roughly 90.7dB(A).

And below Figure 11 shows the same measurement from a more recent CD Player (circa 2000) using a 1bit conversion:

Fig.11 : 999.91Hz @-60dBFS, 1bit CD Player (2000)​

DR is roughly 99dB(A).

But how far can we go with the CD Audio in terms of Dynamic Range?

Our ears hear via hair cells and they don't perceived all frequencies at the same level. Have a look at the Equal Loudness Contour to know more. Taking this into account, engineers develop a technique called "Noise Shaping" which is an advanced dither I already talked about. This technique will spread the low-level noise to where our ears have less sensitivity.

When looking at the Equal Loudness Contour curve, we can see that at 80dBSPL, which is a comfortable listening level, our ears are most sensitive from 500Hz to 4'500Hz. So if we use noise shaping and narrow the THD and noise calculation from 500Hz to 4.5kHz, this is what the software computes:

Fig.12 : 999.91Hz Test tone @-60dBFS with shaped dither, THD and Noise measured from 500Hz to 4'500Hz (16bits/44.1kHz WAV file)​

The above measurement was done directly from the WAV file used for that test. Figure 12 shows that the Software calculates a resolution of 20bits, and the DR is exactly 118.5dB(A) since the full scale tone is exactly 0dBFS when read from the WAV file.
This is why you can read that CD Audio can achieve 20bits equivalent of resolution with the help of noise shaping.

But what if I would do the same measurement without dither, narrowing the analysis the same way? Here you with Figure 13 below:

Fig.13 : 999.91Hz Test tone @-60dBFS without dither, THD and Noise measured from 500Hz to 4'500Hz (16bits/44.1kHz WAV file)​

The Software computes indeed 18bits equivalent of resolution, but we are still far from the 20bits we saw before. To be complete, Figure 14 below shows the same with rectangular dither:

Fig.14 : 999.91Hz Test tone @-60dBFS with rectangular dither, THD and Noise measured from 500Hz to 4'500Hz (16bits/44.1kHz WAV file)​

We've lost 0.6bits of resolution because of the low level noise that the rectangular dither generates and that raises the noise floor equally across the bandwidth.

That is another reason why I use test tones with shaped dither. Indeed, some CD Player have an extremely low noise floor and so will benefit from that noise shaping technique. And therefore I measure them this way too.

Bandwidth​

Bandwidth has always been an important measurement and we like to see it ruling flat. Unfortunately, with our CD Players, we have oversampling filters which try to compensate for the natural attenuation of the sin(x)/x envelope which is a normal effect of the Digital to Analog conversion and is due to the zero-hold function of all DACs.

The zero hold creates the famous stair steps which, if unfiltered, will generate a lot of unwanted aliases out of audio band, but most importantly will also generate a -3.92dB roll-off at 20kHz.

This well explained in Analog Devices Tutorial "Oversampling Interpolating DACs" from which Figure 15 is extracted:

Fig.15 : Unfiltered DAC output shows attenuation of bandwidth due to sin(x)/x envelope and unwanted images​

The oversampling filter will introduce some modification to the bandwidth, like ringing or attenuation at the top end of the frequency, trying to compensate for the roll-off.

I now measure the bandwidth from a long term averaging (500+) of a periodic white noise. This allows me to run this test at 192kHz data input where I'm sure the ADC of my interface is truly flat from 20Hz to 20kHz, so it does not influence the one of the device under test.

Fig.16 : Bandwidth of a Revox B 226-S from periodic white noise (left and right channels)​

Figure 16 shows bandwidth measurement from an old CD Player which had a 4x oversampling filter and exhibits some ringing and a bit of attenuation too. Another advantage of this measurement is that it shows the channel mismatch between left and right, as shown in Figure 16.

Oversampling filter response and attenuation​

As I mentioned previously, all modern DACs use an oversampling filter which not only increased the sampling rate, but more importantly removes the unwanted artifacts of the conversion, due to the zero-hold function of all DACs.

The oversampling filter has an effect on the bandwidth which I already showed, and it is interesting to understand how well it will filter the out of band unwanted noise and distortion.

I perform this measurement using the same periodic white noise (@-10dBFS) test file that I use for the bandwidth analysis.

Fig.17 : Periodic White Noise @-10dBFS from 20Hz to 96kHz, Linear Frequency Scale​

The Figure 17 shows an exemple of filter attenuation. I align the top with 0dB for the ease of analysis. We see that there is a -90dB attenuation performed by the filter, out of band. In addition, we can also verify the beginning of the stop-band attenuation which we see at 24.1kHz on Figure 17.

In addition, I like to overlay a measurement of the AES-DFD Intermodulation test, as it also shows how well the high level 18kHz+20kHz test tones are attenuated. Figure 18 shows an example of such.

Fig.18 : Periodic white Noise and AES-DFD (18k+20kHz 1:1) overlaid, Linear Frequency Scale​

The purple trace of Figure 18 shows the two test tones 18kHz & 20kHz which are well attenuated, as their respective mirror copies (centered around 22.05kHz) at 26.1kHz and 24.1kHz are below -90dB.

For comparison, Figure 18 shows the same measurement from an older Revox B 226-S CD Player, with a 4x oversampling filter.

Fig.19 : Periodic white Noise and AES-DFD (18k+20kHz 1:1) overlaid from a Revox B 226-S, Linear Frequency Scale​

From Figure 19, we see that the copies of 18kHz & 20kHz are much less attenuated as they spike at -56dB and -40dB respectively.
Again, these copies are an effect of the zero-hold function of all DACs, that creates copies of audio band signal by a mirror effect centered at half sampling frequency, which is 22.05khz. And so everything is copied, by mirror effect. A 20kHz, which is 2.05kHz away from 22.05kHz, therefore appears again at 22.05kHz + 2.05kHz = 24.1kHz.

The Analog Devices Tutorial "Oversampling Interpolating DACs" shows that all these images repeat again beyond 44.1kHz as everything from 0Hz to 44.1kHz is copied as such, from 44.1kHz to 88.2kHz (only enveloped into the sin(x)/x function), and that goes on. The oversampling filter tries to filter and reject all of this much further away.

Multitone Tests​

Intermodulation Distortion

I think intermodulation distorsion (IMD) is more interesting that harmonic distortion simply because it's easier to hear! The harmonic distortion hides itself into the music because of its harmonic nature, but it's not case with IMD.

Many tests and standards have been created and I use nearly all of them. They are:

• IMD AES-17 DFD "Analog" (18kHz & 20kHz 1:1)
• IMD AES-17 DFD "Digital" (17'987Hz & 19'997Hz 1:1)
• IMD AES-17 MD (41Hz & 7993Hz 4:1)
• IMD CCIF (18kHz & 20kHz 1:1)
• IMD TDFD (13'58Hz & 19841Hz 1:1)
• IMD TDFD Bass (41Hz & 89Hz 1:1)
• IMD SMPTE (60Hz & 7kHz 1:4)

These are standard dual tones test to identify the interactions between them. There is nice knowledge article on the Audio Precision site, should you want to know more.

I do not usually show any representation of the IMD, except the IMD AES-17 DFD that I use to show the oversampling filter attenuation. Once upon a time, the AES recommended a "DFD Digital" test, which was a 2'010Hz between the two tones instead of the standard 2'000Hz. As you can see above, I still use it.

I run these test at 192kHz input, which allows an analysis of up to 96kHz. Figure 20 shows an example from a Denon DCD-3560 of the IMD AES-17 "Digital" (in Linear Frequency Scale).

Fig.20 : IMD AES-17 "Digital" (17'987Hz & 19'997Hz 1:1), Linear Frequency Scale​

The Software identifies all components part of the intermodulation distortion and sums them. I report the top left value.

The other very classic IMD test is the AES-17 MD (41Hz & 7993Hz 4:1) which, I think, better represents the typical interactions between true musical content, in this case the interactions between a low level tone at 41Hz and a high one at 7993Hz played at a 1:4 ratio. Figure 21 shows an example from the same Denon DCD-3560.

Fig.21 : IMD AES-17 MD (41Hz & 7993Hz 4:1), log scale​

Note that this time, I used a log scale as it makes it easier to read.

Triple Tones

Some CD Players want to shine in specific standard tests. That means they have a code in the signal processing to recognize typical tests, especially dual test tones. For that reason, and to defeat these mechanisms, I run the below triple tone tests:

• Borberly (9kHz, 19kHz, 20kHz)
• Cordell (0kHz, 10kHz, 20kHz)
• Klingelnnberg (10.5kHz, 19kHz, 20kHz)

I do not show them, unless they reveal a trick.

Multitone

This test became quite popular recently because it's much closer to what music is. When listening to it, it sounds like someone playing the organ.

I use a 1/10 decade multitone test which is standard and always report the result. Figure 22 shows an example.

Fig.22 : Multitone 1/10 Decade from a CD Player, Left and Right channels represented​

The multitone test helps to identify if the player clears more of less than 16bits of resolution. Figure 20 shows a very good result of near 110dB free of distorsion.

Crosstalk​

Crosstalk is the level of leakage from one channel to the other. It is performed by sending a full scale tone (0dBFS) on left channel and measuring the right tone. Because Crosstalk from Right to Left channel is often not identical to crosstalk in the other direction, I measure both and report the worst case. This is done regularly at 1kHz, but I do it with 100Hz and 10khz test tones too.

Figure 23 shows an example of crosstalk from left to right channel at 10kHz. The resulting leakage is measured at -114dBFS in the right channel, which is very good (Right to Left channel crosstalk was -117dBFS, not shown).

Fig.23 : Crosstalk from left to right channel at 10kHz measured at -114dBFS​

The crosstalk increases with frequency.

Inter samples over resistance​

Started with the Teac VRDS-20 review, and on your request + support to get it done (more here), I added an "inter-samples overs" test (similar to the one described in the Nielsen / Lund AES paper),which intends to identify the behavior of the digital filtering and DAC when it come to process near clipping signals. Because of the oversampling, there might be interpolated data that go above 0dBFS and would saturate (clip) the DAC and therefore the output. And this effect shows through distorsion (THD+N measurement up to 96kHz):

Intersample-overs tests Bandwidth of the THD+N measurements is 20Hz - 96kHz	5512.5 Hz sine, Peak = +0.69dBFS	7350 Hz sine, Peak = +1.25dBFS	11025 Hz sine, Peak = +3.0dBFS
Teac VRDS-20	-30.7dB	-26.6dB	-17.6dB
Yamaha CD-1 (Non-Oversampling CD Player)	-79.6dB	-35.3dB	-78.1dB
Onkyo C-733	-79.8dB	-29.4dB	-21.2dB
Denon DCD-900NE	-34.2dB	-27.1dB	-19.1dB

Table 1: Inter-sample overs THD+N of several CD Players​

From Table 1, we can see that the Denon DCD-900NE oversampling filter does not have headroom to prevent inter-sample overs. The Yamaha CD-1 shines in that test because it's old enough not to have an oversampling filter.

3DC levels representation​

Stereophile were fond of that test, and I like it too. The intention of that test was to verify if the CD Player would be silent and linear enough to represent the lowest possible level of a digital sample in 16bits/44.1kHz.

Let's do some quick maths to understand what is this level:

• With 16bits we can represent 2 power 16 = 65'563 levels.
• Since the PCM format is signed, we have 32'768 positive and negative levels (in fact only 32'767 positive because there's also the 0 to account for).
• The lowest symmetrical level in 16bits is therefore 1/32'768.
• The formula 20*log(1/32'728) = -90.31dFBS gives us the lowest possible level of a digital sample.

At this level, the FFT of a sine tone (@-90.31dBFS) looks like this:

Fig.24 : 999.91Hz @-90.31dBFS without dither
(Red trace from digital output, blue trace from RCA outputs of a CD Player)​

At this lowest digital sample level, there are only 3 possible levels to represent, -1, 0 and +1. When looking at the FFT, we mainly see odd harmonic content, which means we should see a square signal in limited band (up to 22.05Hz max, i.e. 44'1kHz / 2). And it is better to look at it with a scope:

Fig.25 : 1kHz @-90.31dBFS from the digital output of a Sony CDP-337ESD​

Figure 25 shows the three levels well represented, -1, 0 and 1, with perfect symmetry as this is the digital output. The ringing you see is due to the Gibbs Phenomenon.

Now, let's have a look at the same representation but from the analog output of the same CD Player:

Fig.26 : 1kHz @-90.31dBFS from the digital output of a Sony CDP-337ESD​

From Figure 26, we recognize the 3DC levels, with a good symmetry too, even if they are disturbed by distortion and noise. It means this player is linear and silent enough to go that low with reasonable disruption (which we see as the blue added even harmonics in Figure 24, that are distortion).

This test is somewhat redundant with others that we can perform to look at linearity and low level noise. But I like it because it’s quick to read.

Linearity​

What we call linearity, is the ability for a DAC to reproduce a sine tone at the correct amplitude. If that is an easy exercise for all them when the signal is close to full scale, it becomes a challenge at much lower levels. The reason is that at lower levels, there are less bits to represent the amplitude of the signal and so not only the quantization errors increase but the lowest amplitude signal will suffer more from noise and distortion.

There are multiple ways to look at the linearity. One is to do a sweep at decreasing levels of a sine tone. But depending on the software in use, it might not be possible to look at it this way, especially with a CD Player. Another way is to look at individual sine tones and verify if their level deviates from what is requested.

For that type of analysis, I use dBFS vertical scale instead of dBr, as shown in Figure xx, and for two reasons:

1. It is required to verify the level of the tone, as we are not interested by distortion or noise in that case.
2. Because the interface I use cannot be calibrated to align the 0dBFS of the its ADC to the 0dBFS of the CD Player being reviewed, it is necessary to account for the potential deviation at full scale.

Figure 27 below illustrates this and is a 999.91Hz test tone (without dither) at respectively 0dBFS (orange trace) and -70.31dBFS (violet trace):

Fig.27 : 999.91Hz Sine Tone @0dBFS (Orange trace) and @-70.31dBFS (Violet trace), from a CD Player​

I left the plot of the main tone and you can see the respective levels as captured by the software in the legend. The full scale one is seen at -1.1dBFS which needs to be accounted for when looking at the much lower -70.31dBFS that is captured be the software at -71.3dBFS. It means that the true value is therefore -71.2dBFS, i.e. this player is linear at this level (they all should be).

Note that the above is without dither, and that makes the exercice a lot more difficult for a DAC. All modern DACs (and so CD Players) have a good linearity because they all use dither which became standard with 1bit DACs. But ancient DACs, like the first generations of multibit ones did not use dither by default, and so it's more difficult for them to pass this test, especially when we go lower, at -80.77dBFS and -90.31dBFS which I use too.

That said, modern masters and records all use dither, and in fact even noise shaping technique. That means our ancient DACs will also benefit from dither or noise shaping, except for older records. For these reasons, it makes sense to see how low they all can go.

With dither and noise shaping, it is possible to break the theoretical -90.31dBFS lowest possible level of the 16bits data resolution (which I talked about previously).

Without dither, a sine tone at -90.31dBFS with 16bits/44.1kHz looks like what's shown in Figure 28 below:

Fig.28 : 999.91Hz @-90.31dBFS without dither from the analog outputs of a CD Player​

Figure 29 shows the same with standard dither (of the type rectangular):

Fig.29 : 999.91Hz @-90.31dBFS with rectangular dither from the analog outputs of a CD Player
​

As Figure 29 shows, we have a lot less distortion, and this is with a CD Player from the '80s that had a multibit R2R.

Figure 30 below shows the same with shaped dither, which is a more intelligent way to use low level noise to improve linearity:

Fig.30 : 999.91Hz @-90.31dBFS with shaped noise from the analog outputs of a CD Player​

The distorsion decreased again which means there is an advantage to use shaped noise, and that's why studios have been doing for quite a long time when in need to decrease the bit depth to 16bits.

With all of that, we can the limit of -90.31dBFS and go lower. Figure x31 below shows the same 999.91Hz test tone @-110dBFS with rectangular dither:

Fig.31 : 999.91Hz @-110dBFS with rectangular dither (16bits/44.1kHz), from a CD Player​

If you look close, you'll see that the tone is represented at roughly -105dBFS, for -110dBFS requested. This means we lost linearity. There are no real convention as to when the linearity is lost, some consider as soon as 0.5dB deviation, others up to 2dB.

Now, if we use shaped noise, with the same player as above, we get:

Fig.32: 999.91Hz @-110dBFS with shaped noise (16bits/44.1kHz), from a CD Player​

Figure 32 shows that we are nearly at -110dBFS with the same player, which means we got our linearity back.

Again, modern 1bit DACs use noise shaping technique as it's the only way to limit their quantization noise due to the reduction of the bit depth from 16bits to only 1bit. But ancient CD Players and their associated R2R DACs will benefit from it when it's added to the music, as part of the master.

That is the reason why I measure the linearity of CD Players without dither, with rectangular dither and with shaped noise, as it tells me how they will respectively behave with old or modern masters.

Pitch error​

The pitch error test allows to identify the clock deviation very precisely. Many modern CD Players and DACs are in the range of +-10ppm. This test is a sine tone at 19'997Hz and resulting frequency is measured.

Fig.33 : Pitch error measurement with a sine tone at 19’997Hz, Linear Frequency Scale 20Hz to 40kHz​

Figure 33 shows the result from a 1990 CD Player that is 19'996.39Hz for 19'997.00Hz requested. It means a deviation of -30.5ppm which is reasonable as it is the precision of a standard crystal.

Testing the drive​

Measuring the ability of the CD Player to extract data from the disc is more important than pure performance measurements. What satisfaction would we have with a CD Player unable to read properly a disc that is slightly scratched or that has been created at the limit of the Redbook?

Tracking capabilities are tested as described below:

​

Test type​	Technical test​
Variation of linear cutting velocity​	From 1.20m/s to 1.40m/s​
Variation of track pitch​	From 1.5µm to 1.7µm​
Combined variations of track pitch and velocity​	From 1.20m/s & 1.5µm to 1.40m/s & 1.7µm​
HF detection (asymmetry pitch/flat ratio)​	Variation from 2% to 18%​
Drop-outs resistance​	From 0.05mm (0.038ms) to 4mm (3.080ms)​
Combined drop-outs and smallest pitch​	From 1.5µm & 1mm to 1.5µm & 2.4mm​
Successive drop-outs​	From 2x0.1mm to 2x3mm​

Table 2: Physical tracking tests abilities of a CD player.​

Conclusion

The above was possible after months and months of testing and reflecting on what is of importance when to comes to convert a digital signal from the Compact Disc.

Several respected members of ASR have contributed (@restorer-john, @AnalogSteph, @danadam, @JohnPM, @John_Siau, @Scytales, @KSTR, @JIW, @tccalvin, … I’m sure I missed some but I will update!), providing their feedbacks and insights, thanks ever so much to them. Others have indirectly contributed, @amirm of course, and @John Atkinson who published so much in the past decades and has been an inspiration, from the beginning, to me. Special thanks to my friend @Vintage02 who helped a lot when it came to relate what we hear to what we measure, that was a long journey and a satisfying one.

All to say that I think the tangible performances of a CD player are represented and reflected in the above measurements. What is of importance is left to the reader to decide, with a set of (I hope) exhaustive measurements.

Thanks to everyone who made it that far!

 

[NTTY]

Let me keep that space in case my first message becomes really too long for the forum.

 

[danadam]

The formula 20*log(1/32'728) = -90.31dFBS gives us the lowest possible level

With dither and noise shaping, it is possible to break the theoretical -90.31dBFS lowest possible level of the 16bits data resolution (which I talked about previously).

That level is used (I think) for symmetry between samples at -1, 0 and 1 level and yes, it is the lowest possible level of a digital sample, but it is not the lowest possible level for a signal. The lowest possible level is about -96.32 dBFS. For example, -94 dBFS:

sox -D -r44.1k -n -b16 "sin_999.91_-94dBFS.nd.flac" synth 10 sin 999.91 norm -94

and -96 dBFS:

sox -D -r44.1k -n -b16 "sin_999.91_-96dBFS.nd.flac" synth 10 sin 999.91 norm -96

You'll notice that the amount of quantization distortion made the level a few dB higher in the first case (-92 dBFS) and a few dB lower in the second case (-99.5 dBFS).

 

[NTTY]

You’re right, and thanks for the files, as always, I’ll play with them. I will need to update my text with your feedback.