# God of SINAD vs. reality we get from most available music files

#### Vacceo

##### Major Contributor
Really folks. Go do something else with your time. Fighting SINAD is like fighting with a restaurant to not have clean dishes. It is not like your food would be cheaper if they served your food on dirty ones.
I want to please keep you in the room for a second because I have questions. Before the dishes analogy you have said that it costs nothing to increase the SINAD to 115 db (top best human audiblility in best case hearing scenario, right?) and this is evidenced by a nice amount of affordable amps and dacs that reach or surpass those numbers.

If that is the case (I don´t dispute the fact), why manufacturers have not adopted those practices massively? The best example I can think of are AVR and AVP, whose SINAD we cheer when it reaches 100 db or close, which is not that common. What am I missing?

#### Jim Taylor

##### Major Contributor
For a device to not cost you more than 0.5 dB of SINAD, it needs to have a SINAD that is 10 dB higher than your content. So even if you arrive at 93 dB being SINAD of 16 bit music, your hardware needs to have a SINAD of 103 dB.

I don't understand where the 10 dB figure comes from. Why ten? Jim

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#### DonH56

##### Master Contributor
Technical Expert
Forum Donor
I don't understand where the 10 dB figure comes from. Why ten? Jim
Assuming uncorrelated noise and distortion, then you can root-sum-square the noise contribution of devices in a chain. For example, start with a device having -100 dB SNR. Now cascade another device with -110 dB SNR, with everything at unity gain. The resulting SNR will be about -99.586 dB, meaning 10 dB lower SNR has cost about 0.5 dB in SNR.

Recall dB = 20*log10(V2/V1) for voltage, so referenced to V1 = 1 V we find V2 = 10^(dB/20).

Now for two signals Va and Vb calculate the net SNR:

SNR(net) = 20*log10( sqrt(Va^2 + Vb^2)) = 20*log10(sqrt( (10^(-100 dB/20))^2 + (10^(-110 dB/20))^2))) = -99.586 dB

More involved explanation in this long, ugly thread: https://www.audiosciencereview.com/...opagate-through-my-system.33358/#post-1165118

HTH - Don

#### amirm

Staff Member
CFO (Chief Fun Officer)
If that is the case (I don´t dispute the fact), why manufacturers have not adopted those practices massively? The best example I can think of are AVR and AVP, whose SINAD we cheer when it reaches 100 db or close, which is not that common. What am I missing?
AVRs have mandatory DSP which costs them at least 10 dB.

#### Jim Taylor

##### Major Contributor
Assuming uncorrelated noise and distortion, then you can root-sum-square the noise contribution of devices in a chain. For example, start with a device having -100 dB SNR. Now cascade another device with -110 dB SNR, with everything at unity gain. The resulting SNR will be about -99.586 dB, meaning 10 dB lower SNR has cost about 0.5 dB in SNR.

Recall dB = 20*log10(V2/V1) for voltage, so referenced to V1 = 1 V we find V2 = 10^(dB/20).

Now for two signals Va and Vb calculate the net SNR:

SNR(net) = 20*log10( sqrt(Va^2 + Vb^2)) = 20*log10(sqrt( (10^(-100 dB/20))^2 + (10^(-110 dB/20))^2))) = -99.586 dB

More involved explanation in this long, ugly thread: https://www.audiosciencereview.com/...opagate-through-my-system.33358/#post-1165118

HTH - Don

Thank you! Jim

#### Vacceo

##### Major Contributor
AVRs have mandatory DSP which costs them at least 10 dB.
I guess that given time, we´ll see avr´s pushing the numbers if not to 115 db or more, at least systematically above 100db (a bit more than CD quality, which is not bad).

#### Cbdb2

##### Addicted to Fun and Learning
I guess you have never listened to Slayer.
Slayer is not the same as "rock in any variant". Distortion can be a tool. I guess you've never listened to electric guitar.

#### Blumlein 88

##### Grand Contributor
Forum Donor
snipppage........

3. Many people including myself play > 16 bit content. MQA research in process of encoding millions of tracks for their format shows that the best case dynamic range is about 18 bits, not 16 as you assume. And this is analyzing real content/music.
snippage
I'd like a list of these 18 bit dynamic range recordings. Other than studio only synthetic music I've not found anything better than 12 bits or close to 70 db.
7. There is no such thing as single number noise SPL for microphones, rooms, etc. Such noise highly varies with frequency so any simplified statement about them is wrong. Again, read peer reviewed research papers from Fielder and Stuart. Or watch my video on the same:
That kind of works both ways. Room noise with a single number like 30 db spl doesn't mean in the range of our most sensitive hearing we cannot still hear down near 0 db SPL. A device that has merely a 90 db Sinad figure is also sometimes like that having a much lower level in that 3-5 khz range. Or it could be 90 db THD and noise is much lower when the spec is Sinad. At least on speakers the device may be fine. I listen much less on headphones so I'll not comment on that.

I agree with cheap DACs having Sinad of -110 db or better the point is moot. However, we aren't there with AVRs. When you get to AVRs I agree with what you say above: There is no such thing as a single number. Yet isn't that what Sinad is, a single number that over-simplifies? Plenty of AVRs come in with Sinad in the mid or low -80 db range. If that is noise it probably isn't good enough. You'll hear it. If on the other hand it is distortion and noise is a good bit lower it is fine. Just looking at Sinad you'll not know which is which.
Really folks. Go do something else with your time. Fighting SINAD is like fighting with a restaurant to not have clean dishes. It is not like your food would be cheaper if they served your food on dirty ones.
Sinad has its place, but I don't like the one number. I'd prefer noise and THD listed separately. And in your reviews there are graphs to show us both. If Sinad is low enough you don't have to worry, but it is in non-SOTA devices that the one number is an over-simplification.

#### Vacceo

##### Major Contributor
Slayer is not the same as "rock in any variant". Distortion can be a tool. I guess you've never listened to electric guitar.
There is no such a thing as clean and pristine electric guitar sound by definition. That is what an acouistic guitar is.

#### Blumlein 88

##### Grand Contributor
Forum Donor
I don't understand where the 10 dB figure comes from. Why ten? Jim

Put some numbers in here and see what the results are. Here is another version for more than one source.

#### Jim Taylor

##### Major Contributor

Put some numbers in here and see what the results are. Here is another version for more than one source.

This forum should be called "The Bakery". There are some pretty smart cookies around here. Jim Taylor

#### Blumlein 88

##### Grand Contributor
Forum Donor
This forum should be called "The Bakery". There are some pretty smart cookies around here. Jim Taylor
Hey the smart cookies are part of why I keep coming around here. I've learned a lot from them.

I'm even thinking of my Macadamia White chocolate cookies right now since you brought up cookies.

#### restorer-john

##### Master Contributor
We know that once the SINAD numbers are getting well over 110dB, neither noise or distortion are an issue, regardless of the product type in question. We have DACs with effective residual noise figures around a microvolt or so, which is truly incredible if you ask me. We have amplifiers that are plumbing low double or even single figure residual noise levels. Amazing.

Personally, I'd rather see residual noise figures and THD figures quoted separately, with the noise figure's bandwidth stated, but I can also see a good reason to keep it simple with a single metric.

In short, there's nothing bad about chasing a better SINAD number. Does it tell the whole story? No.

#### poxymoron

##### Active Member
God of SINAD vs. reality we get from most available music files

There is a good thread here in ASR discussing the practical importance of SINAD number

which links to the original article at

Let me quote from that article:

“SINAD is short for “Signal to Noise And Distortion”. It’s the ratio between the signal - the stuff we want to hear, like the music we play - to all the other things we don’t want in the sound. It’s also sometimes expressed as THD+N, or “total harmonic distortion plus noise”, which is the ratio of the noise and distortion to the signal - the same thing the other way around.
As the name suggests, SINAD is a sum of two broad groups of things we don’t want in the sound: Noise, and distortion. Noise is just what it sounds like: noises leaking into your music, which can range from the “hum” of your AC power, to the “hiss” of white noise. There are a lot of potential sources of noise out there, and they can distract from what you actually want to listen to, particularly if you’re listening quietly.
Distortion, the other part, is similar to noise in that it’s an addition to your music. Unlike noise, however, distortion is produced by your music interacting with the flaws of the system. This means that distortion will be related in level to the signal causing it, whereas - as anyone who’s heard hiss on their IEMs will know - noise can be loud without anything playing at all.
This is the big trouble with SINAD: In some cases, a low score points to an amplifier or DAC that is just plain not working, but in others, it’s only catching “problems” that you won’t actually be able to hear.”

Obviously, the SINAD, or THD+N, which is absolutely same thing just with opposite sign, is not well understood or simply not understood in general public, as we can see from many threads here in ASR. Let me name a few:

SINAD is appealing for both inexperienced readers and technically oriented reviewers as it gives a single number that is used in simplified charts as a comparative measure of various audio products. As any simplification, there is a question if such simplification is good enough to be a basis of comparisons of audio products. It definitely tells something, but how would it be useful in a real life?

Let's thing, for a while, about music files that we use to feed our beloved audio chains. Streaming services yield files of unknown quality, regardless label like “lossless”, “hires” etc. File analysis often shows that such label is incorrect. In fact, well prepared “old style” 44.1kHz/16bit files are still a very good source of music and many so-called “hires” files and streams are just a re-sampled versions of original 44.1/16 versions. The other point to be mentioned is that a background noise during recording and microphone path noise are barely that low to utilize dynamic range of the 44.1/16 format. In fact, the best recordings only attack only 60dB range, and this is for classical music.

View attachment 222728

Popular music often sticks with something like 20dB range. So, there is a question, what SINAD we can get from 44.1kHz/16bit files, just in theory? And after processing by a DAC?

1. Analysis of 44.1kHz/16bit files with respect to achievable SINAD

SNR of 16bit full scale sine wave to the rms value of quantization noise in theory is:
SNR = 6.02N + 1.76dB

For N = 16 (bits) we get SNR = 98.08 dB, theoretical maximum

With 1kHz undithered sine in 44.1kHz/16 bits we measure

View attachment 222718

This makes SINAD = 97 dB, THD = -101 dB, but SFDR (spurious free dynamic range) is suffering at some 104 dB due to quantization noise and this quantization noise becomes audible at low level signals like -60 dBFS.

To get rid of spurious frequency components of quantization noise we add a small amount of noise called dither. Frequency independent TPD dither makes a good job of reducing THD, increasing SFDR at the expense of about 4.8dB loss of SNR. Spectrum of 1kHz TPD dithered 44.1kHz/16bit sine looks like this:

View attachment 222719

We get THD = -126.7 dB, SFDR of some 132 dB and SINAD = 93.3 dB.

There are attempts to use dither methods that are not frequency independent. They are based on assumption that noise is most audible in certain frequency range, so they reduce noise rms level below some 12 kHz at the expense of fast rise in noise energy between 12 kHz and 20 kHz. We call this noise shaping and the spectrum of 1kHz sine wave with noise shaped dither in 44.1kHz/16bit format looks typically like this:

View attachment 222720

We get THD = -104.1 dB, but SFDR of 102 dB and SINAD only 70.7 dB, measured over 22 kHz bandwidth without frequency weighting. Noise shaping is responsible for this huge SINAD loss and the reason is we have only 44.1kHz sampling, i.e. 22.05 kHz BW. Noise shaping would be more effective only at higher sampling rates like 96 kHz.

There might be an idea of resampling the 44.1kHz/16bit source file to higher sampling rate and using noise shaping, but once we have a 44.1kHz/16bit original file, a little to improve SNR or SINAD can be done, resulting only in one or few dB difference. No DAC with 130 dB SINAD would make any miracle here.

As a comparison, next plot shows all the previously discussed files – undithered, TPD dithered and noise shaped 1kHz sine in 44.1kHz/16bit format in one graph.

View attachment 222721

2. 1kHz sine waves in 44.1/16 format played through through an oversampling DAC, Topping D10s

Audiophiles, supported by popular audio reviewers, often assume that playing “low resolution” 44.1/16 format files through some miraculous oversampling DAC that oversamples at 384kHz/32bit will get something more from 44.1/16 files. Unfortunately, not really. We may get some tiny improvement in some cases, but in fact the format of the music file is a bottleneck. Let's see how it works. The analog output of Topping D10s was digitized by E1DA Cosmos ADC, the files from previous examples were used to feed the Topping DAC. ADC sampling was 96kHz/24bit, bandwidth of SINAD evaluation was 22kHz.

First, let's see what we get when the DAC – ADC chain is supplied with a 44.1kHz/32bit float 1kHz sine.

View attachment 222722

We get THD = -125 dB, SFDR of 128 dB and SINAD = 110.7 dB. This is enough to handle 16 bit test signals. This was shown only as a comparison, this is NOT a 16 bit signal.

We start measurements with 1kHz undithered sine in 44.1kHz/16 bits

View attachment 222723

We get THD = -101.5 dB, SFDR of 106 dB, SINAD = 97 dB. So we are at almost same numbers as for the test signal itself.

Next is TPD dithered 1kHz sine

View attachment 222724

We get THD = -123.2 dB, SFDR of 128 dB and SINAD = 96.6 dB. Compared to a signal itself, we get slightly worse THD and SFDR but slightly better SINAD (of 3.3 dB), probably a result of oversampling?

The last one is noise shape dithered 1kHz sine

View attachment 222725

We get THD = -103.9 dB, SFDR of 103 dB and SINAD = 75 dB. Again slightly better SINAD.

And the all-in-one plot for the DAC – ADC chain

View attachment 222726

3. Conclusion

Regardless the highest achieved SINAD of the DAC, it is the music file format that will define the theoretical maximum SINAD of our audio chain and worse, it is the background noise of the recording session and microphone path noise that in fact define the SINAD, not speaking about speakers and listening room. As a matter of fact, well engineered CD player is indistinguishable from the best SOTA DACs.
I'll be honest, I've not fully read your entire post, but I will. We'll done, a lot of work. But surely the higher SINAD to start with will allow you to maximise what you can get out of each recording?

#### amirm

Staff Member
CFO (Chief Fun Officer)
I'd like a list of these 18 bit dynamic range recordings. Other than studio only synthetic music I've not found anything better than 12 bits or close to 70 db.
I am not working for MQA so don't know why you are asking me for the list. They exist which is what is important here.

As to 12 bit dynamic range, how did you determine that? This is not a trivial thing to compute (MQA uses statistical analysis). And even if you did, you have to break it down by spectrum.

#### amirm

Staff Member
CFO (Chief Fun Officer)
Sinad has its place, but I don't like the one number. I'd prefer noise and THD listed separately.
It is trivial in just about every case to tease them apart. Indeed I do that in almost every review post SINAD measurement. I also show pure dynamic range so that is another way to determine it.

The key about THD+N is that it is an industry standard. THD by itself is not. Even if THD was available, it is the spectrum of it that determines audibility. So the argument shifts to that. SINAD by incorporating both distortion and noise, forces companies to do well in both department not one.

As far as I can tell, none of the people complaining about SINAD have pure motives (not addressing you but OP). They start with being annoyed with the notoriety that it has gotten and then go from there. As I explained, it is a silly armor to wear. It encourages mediocracy in equipment design which results in no benefit to the consumer.

#### Blumlein 88

##### Grand Contributor
Forum Donor
I am not working for MQA so don't know why you are asking me for the list. They exist which is what is important here.

As to 12 bit dynamic range, how did you determine that? This is not a trivial thing to compute (MQA uses statistical analysis). And even if you did, you have to break it down by spectrum.
I thought perhaps you'd know some of them. MQA does a lot of shapeshifting on their claims so I'm not happy giving them benefit of the doubt.

Here is the paper where that info came from without details on the recordings analyzed.

It is unclear, but perhaps that paper refers to this as the quietest they found. Or at least it is among the quieter recordings and is graphed in the above paper.

Anyone around here happen to have this recording?

There is also a CD version though the paper by Stuart and Craven used the DVD with a 192 khz 24 bit recording.

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#### Ron Party

##### Senior Member
CPH (Chief Prog Head)
I'd like a list of these 18 bit dynamic range recordings. Other than studio only synthetic music I've not found anything better than 12 bits or close to 70 db.

IIRC, Arny posted the highest he had ever measured was ~82 db and that it was a BIS disc.

#### tmtomh

##### Major Contributor
@pma 's concern here would be easier to take seriously if the alternative were something other than running 20kHz square waves through Class D amps.

MAB

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