Sure!
Firstly, we can show it by simply looking at the impulse response. Here's what a NOS impulse would be expected to look like:
Output rises to the value of the sample, holds, and then moves back down to value of next sample. No oversampling or interpolation, resulting in a square output IR.
This for example is the impulse response recorded from the Phasure NOS1A dac:
Exact behaviour described above, only difference from the theoretical is that the transition is limited by slew rate of the dac and there is a little overshoot on the square wave likely due to impedance matching or something.
If there is analog reconstruction or a low pass filter then it will look something like this:
Still the described sample and hold behaviour, just with visible LPF modifications as you would expect (interesting visual/interactive demo of this is available here:
https://demonstrations.wolfram.com/ResponseOfLowPassRCFilterToPeriodicWaveforms/ )
And yet when we go to denafrips 'NOS', we see this:
No NOS/Sample and hold behaviour at all, it is simply linearly interpolating from sample to sample.
In fact, if we record this at a 2.5mhz sample rate on the APx555 we can see this:
A stepping behaviour at 32x the 44.1khz sample rate being fed to the DAC. Implying it is oversampling at a 32x rate, and using linear interpolation.
This means if we play something such as a 15khz sine wave, then you can clearly see the linear interpolation between samples:
Secondly - Demonstrate by change in slew/transition time dependent on sample rate.
If it were NOS, slew rate would be identical for any sample rate. It would simply move up to the value of the sample at the fastest rate it can. However because it is interpolating, adding extra samples in, it moves at a different rate dependent on the time between samples/sample rate.
44.1khz:
192khz:
Much faster! Even though it shouldn't be
This is already quite conclusive, but just to be sure, we can prove it mathematically as well.
Linear Interpolation gives a squared sinc frequency response
PI/2 ( so 22.05k @ 44.1k sample rate ) SIN(PI/2) / (PI/2) gives us -3.9dB droop for a NOS
PI/2 ( so 22.05k @ 44.1k sample rate ) (SIN(PI/2) / (PI/2))^2 gives us -7.84dB droop for a for a linear interpolate
(Note graph is offset about 0.2dB)
Can see here that the may in NOS behaves exactly as the maths for NOS would predict.
And the Ares 2 does not, instead behaving exactly as the maths for linear interpolation oversampling would predict. Rolling off at -7.84dB by 22.05khz (almost 4dB more than NOS)
So yes, denafrips 'NOS' is simply linear interpolation oversampling. It is not actually NOS.
One final thing, in John Atkinson's linearity measurements, denafrips' DSP prevented the measurement from working properly, showing that there is signal processing/alteration happening. Though this is hardly unexpected, denafrips literally has their 'DSP board' in the dac. And has revised it several times.
And just to be clear: This is NOT me saying 'grr denafrips bad'. Far from it. I like denafrips dacs and I think that some especially the Ares 2 are amazing value for money.
I just hate misleading or dishonest descriptions/features/specs on products.