The Well-Tempered Computer

Highres recordings

High-resolution (Highres for short) recordings in general are 24 bit and have a sample rate greater than 44.1 kHz.

 

The difference with a normal recording ( 16 bits / 44.1 kHz sample rate) are discussed here.

 

Can your gear resolve a highres recording?

Sample rate

Let’s do some calculations (always tricky in my case)
Playing 192 kHz is 1/192.000 sample per second= 0.000005208333333333330

If the clock driving the DAC has an intrinsic jitter of 10 nano seconds then time step produced at DA conversion fluctuates between:
0.00000001 = 10 ns
0.000005218333333333330 +10 ns
0.000005208333333333330
0.000005198333333333330 -10 ns

Obvious the fluctuations in clock speed are pretty close to the time step.

Ok, let’s use a better clock, one with an intrinsic jitter of 1 pico second.

0.000000000001 = 1 ps
0.000005208334333333330 +1 ps
0.000005208333333333330
0.000005208332333333330 -1ps

 

In this case the variations in the time step look more decent.

The higher the sample rate the more import low jitter values become.

Of course jitter performance is far more complex but it looks like even a clock with a low intrinsic jitter of 1 ps is not able to generate the correct time step.
Therefore, our gear can’t play 192 kHz with the right timing!

Bit depth

If we have a 16 bits recording, there are 2^16=65536 steps.
If we have a 24 bits recording, there are 2^24=16777216 steps.

If the maximum output of our DAC is 2 V, the output will fluctuate between +2 and -2 so a range of 4 V
At the analog site of the DAC we have a step size of
4/2^16=0.0000610351562500000000000 V
4/2^24=0.0000002384185791015620000 V

 

Any DAC able to resolve 0.000000238418579101562 V exactly?

 

For a long time the answer has been no.
Today (2020) there are DAC’s that are linear up to bit 24.
Likewise their noisefloor is extremely low.
The linearity of a DAC is discussed in more detail here.
In practice the noise of the recording chain (mics, mixing console, AD converter) is often much higher. A recording with effectively 20/21 bits musical information is probably the best you can get.

 

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