MQA technical analysis

[mansr]

Check out Bob Stuarts blog for technical MQA talk:

 

MQA Playback | Bob Talks

 

Very funny.

[audiventory]

As I already said, it was an example. The specific value has no significance.

 

 

 

I thought I already did, but lets take it step by step, again using -140 dB/Hz as the example noise floor:

 

1. Convert dB to linear units: -140 dB = 10 ^ (-140 / 10) = 1e-14

2. Multiply by the bandwidth in Hz: 1e-14 * 24000 = 2.4e-10

3. Convert linear to dB: 10 * log10(2.4e-10) = -96.2 dB

 

A noise floor of -140 dB/Hz over a 24 kHz bandwidth thus corresponds to a total noise level of -96.2 dB.

 

When noted noise floor as 6 dB * [bit number] there meant formula dB by level:

 

Level_dB=20*log10([absolute level]/[reference level]).

 

You used formula by power dB

 

Power_dB=10*log10([absolute power]/[reference power]).

 

If 10 replace to 20, where need, we get -52 dB in goal 3.

[mansr]

When noted noise floor as 6 dB * [bit number] there meant formula dB by level:

 

Level_dB=20*log10([absolute level]/[reference level]).

 

You used formula by power dB

 

Power_dB=10*log10([absolute power]/[reference power]).

 

If 10 replace to 20 we get -52 dB in goal 3.

 

The 20 comes from the power being the square of the amplitude. Aren't you supposed to know all this?

[audiventory]

The 20 comes from the power being the square of the amplitude. Aren't you supposed to know all this?

 

Yes. However, you use absolute values. At spectrum analyzer level dB are showed.

 

Me seems, need begin from other end.

 

Need calculate rounding error energy and distribute it across band.

 

As result you get tone with amplitude lower 0 dB (0 dB minus energy of rounding error).

 

The rounding error energy distributed by full band.

 

Wider band - lower energy per Hz.

 

However, analizer use FFT. So need distribute noise by [FFT length]/2 points, not per Hz.

[mansr]

Yes. However, you use absolute values. At spectrum analyzer level dB are showed.

 

Me seems, need begin from other end.

 

Need calculate rounding error energy and distribute it across band.

 

As result you get tone with amplitude lower 0 dB (0 dB minus energy of rounding error).

 

The rounding error energy distributed by full band.

 

Wider band - lower energy per Hz.

 

The calculation is reversible. It doesn't really matter if you work in amplitude or power as long as to stick to one.

 

However, analizer use FFT. So need distribute noise by [FFT length]/2 points, not per Hz.

 

With an FFT you get frequency bins covering a fixed range each. The output is typically normalised to get values that are not dependent on the transform size.

 

Can we now please get back to MQA and away from elementary calculus?

[audiventory]

The calculation is reversible. It doesn't really matter if you work in amplitude or power as long as to stick to one.

 

You are right.

 

With an FFT you get frequency bins covering a fixed range each. The output is typically normalised to get values that are not dependent on the transform size.

 

At spectrum we view power in each point (bin?) of FFT. More points, lesser energy in each one, because sum of quantization errors for all points is constant.

 

Lesser energy for each point - lesser noise floor.

 

Example:

 

Let suggest, total energy spectrum: 100 = 90 (signal) - 10 (errors)

 

Signal take 1 point. 10 (errors) distributed by rest points.

 

If rest 255 point: energy per point is 10/255.

 

If rest points is 1023: energy per point is 10/1023.

 

Etc.

 

It in the each point we will see lesser noise for more FFT length.

 

Can we now please get back to MQA and away from elementary calculus?

 

Ok. We can don't discuss more about the analyzer. But its results of measurements so far from my experience and a bit theory what I know.

I suspect, need check the analyzer’s scaling before using.

[mansr]

At spectrum we view power in each point (bin?) of FFT. More points, lesser energy in each one, because sum of quantization errors for all points is constant.

 

Lesser energy for each point - lesser noise floor.

 

Example:

 

Let suggest, total energy spectrum: 100 = 90 (signal) - 10 (errors)

 

Signal take 1 point. 10 (errors) distributed by rest points.

 

If rest 255 point: energy per point is 10/255.

 

If rest points is 1023: energy per point is 10/1023.

 

Etc.

 

It in the each point we will see lesser noise for more FFT length.

 

That's why the output is usually scaled according to the FFT length.

[audiventory]

That's why the output is usually scaled according to the FFT length.

 

Yes, scaled. But I wrote about spectrum energy distribution. It is relative. Signal (90% energy) anyway take 1 point and 10% energy (errors) distributed by rest points.

[mansr]

Yes, scaled. But I wrote about spectrum energy distribution. It is relative. Signal (90% energy) anyway take 1 point and 10% energy (errors) distributed by rest points.

 

Only if the signal falls exactly in the centre of one of the bins. This is one reason windowing is used.

[audiventory]

Only if the signal falls exactly in the centre of one of the bins. This is one reason windowing is used.

 

If it (we talk about pure sine only) fall between two points it distributed between these points and noise distributed between rest again.

 

Of course, if we have too low point number (16 as example) there more noise will mixed with the sine in its points.

 

I'd like, check the above mentioned source and decoded signals in an other analyzer, that show more traditional results.

 

I try check my results different ways for decreasing of error probability.

[mansr]

If it (we talk about pure sine only) fall between two points it distributed between these points and noise distributed between rest again.

 

Of course, if we have too low point number (16 as example) there more noise will mixed with the sine in its points.

 

I'd like, check the above mentioned source and decoded signals in an other analyzer, that show more traditional results.

 

I try check my results different ways for decreasing of error probaility.

 

What do you consider "traditional" results?

[audiventory]

What do you consider "traditional" results?

 

For 15 bit (truncated 16 bit) sine I expect -90 ... -110 dB (accounting accumulation, overlapping, FFT len (2048 ... 4096) and dithering).

[mansr]

For 15 bit (truncated 16 bit) sine I expect -90 ... -110 dB (accounting accumulation, overlapping, FFT len (2048 ... 4096) and dithering).

 

The total noise power should be somewhere in that range, yes. Not the power per Hz.

[audiventory]

The total noise power should be somewhere in that range, yes. Not the power per Hz.

 

I told about average level of noise floor that we can observe at spectrum plot.

[mansr]

I told about average level of noise floor that we can observe at spectrum plot.

Well, your numbers don't add up. Mine do.

[audiventory]

Well, your numbers don't add up. Mine do.

 

I'd check the file via several other analyzers. But it is not recommendation for you, of course.

 

1. What is length of the file in seconds?

 

2. What is FFT params?

[Foggie]

Check out Bob Stuarts blog for technical MQA talk:

 

MQA Playback | Bob Talks

 

IOW mp3 + gain = MQ$

 

 

Sent from my iPhone using Computer Audiophile

[witchdoctor]

Good video on MQA

 

[Ran]

"Comments are disabled for this video.".....

[mansr]

Good video on MQA

 

Please stop posting links to marketing material. This thread is for actual technical aspects of MQA.

[Miska]

I suppose, the integration can't decrease level noise to 40 dB.

 

What is level (in dB) of the signal (by oscillogramm) in LFSU scale?

 

Level of random noise is directly dependent on length of the FFT (as well as the other parameters). More frequency bins you have, lower the level of random noise is per bin. Level is constant, you just choose how many bins you distribute it to.

[mansr]

Level of random noise is directly dependent on length of the FFT (as well as the other parameters). More frequency bins you have, lower the level of random noise is per bin. Level is constant, you just choose how many bins you distribute it to.

Exactly, and that's why you typically normalise the values so outputs of FFTs of different lengths can be readily compared.

[Miska]

Exactly, and that's why you typically normalise the values so outputs of FFTs of different lengths can be readily compared.

 

Hmmh, discrete tones give pretty much same levels on all cases, but random not, so what do you normalize?

[audiventory]

Level of random noise is directly dependent on length of the FFT (as well as the other parameters). More frequency bins you have, lower the level of random noise is per bin. Level is constant, you just choose how many bins you distribute it to.

 

Level noise depend on FFT length. I wrote about it.

 

[ATTACH=CONFIG]33014[/ATTACH]

 

But at spectrum for 1 kHz sine in 15 bit almost flat noise floor at -140 dB in full band 24 kHz.

 

Blue line looks like 24 bit sine with long FFT, good window and accumulations.

 

Level of the sine about -20 dB at spectrum. There dither is applied to 15 bit, as Mansr wrote.

 

For so flat noise floor, I expect, it will at level about -3 dB (sine have amplitude -3 dB).

 

I expect level noise about -110 ... -115 dB in the best case.

 

Without dither, I expected, -100...-110 dB noise floor.

 

If there will not errors of quantization, level "stick" of the -3 dB sine should be -3 dB at spectrum.

 

May be on the graph need correct bias of zero dB? I.e. need normalize to FFT length, as example?

[Archimago]

I see a few advertising links being offered on this thread...

 

Permit me to offer a non-advertising link for those interested in some objective analysis:

COMPARISON: Hardware-Decoded MQA (using Mytek Brooklyn DAC)

 

Good job on the examination of the underlying code, everyone. Perhaps I missed it in this thread, but I am curious about the filter being used by the MQA decoder. Was there an updated sine sweep looking at the aliasing/nonlinear distortions?