Where does quantization noise come from.

[antcollinet]

Play, for example, a mellow sine tone (200 or 400Hz) at -100dB, using the REW generator. This can only be done in 24bit, obviously. Put your ear next to the mid-woofer and be surprised by how differently DACs handle this task. Or, by how drastically adding dither (also in REW) will improve the result in virtually all cases.

In this case your SNR is only around 20dB even with the very best DACs. So yes - DACs of varying capability will handle it very differently (even Good Dacs may be down at 0dB SNR with this test)

(except in extreme/unrealistic circumstances)

 

[William H.]

About Noise

Since perfect DACs cannot exist, noise is always present. The issue is: when does the level for the parameter estimates uncertainties become irrelevant?

There are two different types of noise for non-quantum systems.

Time Dependent Noise - The errors between a state of nature[1] and the data values (or the uncertainty in parameter estimates from the data) vary with time. Typically the noise is is pseudo random. Time dependent noise can be informative. (pink noise vs white noise vs brown noise).

Time Independent Noise - The errors between a state of nature and the data values are constants. The a simple example is a DC offset in the signal.

Digitazation attempts to model inherently continuous data by indiscreet means. Even when time dependent and time independent noise levels are low, the digitized signal is a only a model for the original signal (a state of nature). The analog signal noise properties clearly affect the parameter estimate errors in the digital data. However the primary issue is the mathematical model for the data must map onto the analog signal in a strict 1:1 mathematical relationship. A common example of this type of problem is aliasing.

1. A state of nature refers to the fact that nature knows the precise values for the parameters of interest. The signal (data) and the mathematical model for the signal only provide parameter estimates. Noise is the difference between a parameter estimate and the true (but unknown) value.

 

[Chromatischism]

Noise (signal processing) - Wikipedia

en.m.wikipedia.org

Scroll down to Types of noise and you will see Quantization Error.

 

[William H.]

And?

 

[William H.]

Quantization error (QE) is a type of time independent noise. QE is caused by unavoidable uncertainties in converting the digital input into analog voltages. There are two types of QE - offset error and gain error. Both error levels approach zero as the digital signal bit depth approaches infinity. Otherwise, for a given bit depth QE is proportional to digital signals’ least significant bit percent.

DAC voltage estimates are also affected by time dependent noise sources. How much DAC op amp conversion speeds and op amp gain fluctuate over time depends on both circuit component quality and circuit design. Op amp output can exhibit time independent gain errors as well.

Since we’ve gone this far, DAC performance is also degraded by clock jitter noise. Jitter is the uncertainty or error in sample clock time intervals due to short term clock signal phase variations. The result is the clock signal oscillation amplitudes’ positions are offset from their intended points in time. Clock jitter has both time dependent and time-independent components. Clock jitter is noise is caused by clock circuit phase noise, power supply noise, circuit cross talk and Johnson-Nyquist noise and even mechanical vibrations. Time dependent, high frequency, clock jitter can degrade DAC dynamic range due to dropped bits.

 

[antcollinet]

Quantization error (QE) is a type of time independent noise. QE is caused by unavoidable uncertainties in converting the digital input into analog voltages. There are two types of QE - offset error and gain error. Both error levels approach zero as the digital signal bit depth approaches infinity. Otherwise, for a given bit depth QE is proportional to digital signals’ least significant bit percent.

DAC voltage estimates are also affected by time dependent noise sources. How much DAC op amp conversion speeds and op amp gain fluctuate over time depends on both circuit component quality and circuit design. Op amp output can exhibit time independent gain errors as well.

Since we’ve gone this far, DAC performance is also degraded by clock jitter noise. Jitter is the uncertainty or error in sample clock time intervals due to short term clock signal phase variations. The result is the clock signal oscillation amplitudes’ positions are offset from their intended points in time. Clock jitter has both time dependent and time-independent components. Clock jitter is noise is caused by clock circuit phase noise, power supply noise, circuit cross talk and Johnson-Nyquist noise and even mechanical vibrations. Time dependent, high frequency, clock jitter can degrade DAC dynamic range due to dropped bits.

All of which is great information. However the effects of all of this can be measured on the output of a DAC, and none of it is an audible issue in modern well designed DACs, which are in the vast majority.

 

[William H.]

... However the effects of all of this can be measured on the output of a DAC, and none of it is an audible issue in modern well designed DACs, which are in the vast majority.

Agreed.

My goal was to address the original poster's comment "but I can't get my brain around where the noise comes from!"