You have the means, perhaps you can do the experiment yourself and make a YouTube video. hook up a signal generator to an oscilloscope and then output to an A/D and then right back to analog via D/A and then hook the output to another oscilloscope. You will see without fail the signal at the other end of the D/A is a perfect sine wave up to 22khz if you sample at 44.1khz.
It isn't the same upto 22khz. That'd only be true if we have a reconstruction filter that doesn't attenuate anything at all below the Nyquist frequency.
This is somewhat easy to do, but usually means you're then not attenuating by Nyquist, because you're rolling off too late. So whilst your amplitude for signals under 20khz might be mostly correct, you're also producing unwanted images of the signal and not accurately reconstructing. Filters are a game of tradeoffs unless you throw more and more compute power at the problem (which is kinda what Chord does).
Let's take an example DAC, in this case the ESS 9039 based SMSL SU-9 Pro.
Selecting the 'fast linear' filter, we can see that a 1khz 0dBfs sine outputs 4.192V. I've set the dBrA ref level to this so we can easily see how gain changes.
If we now go for 17khz, you can see that the level is sliiiightly lower, also there are some unwanted products showing up above the fundamental. Some of which (the ones at 34khz and 51khz) are just the harmonic distortion of the DAC, but the other one is actually due to the incorrect reconstruction filter.
And if we go for 22khz the main signal is a tiny bit lower as the filter continues to gently roll off, though again only by a tiny amount so that indicates the filter is not attenuating things much at all here, though we now have a substantially higher distortion product just above the fundamental as well.
So why is this? Well it's because the filter is not actually adhering to Nyquist, as it is not attenuating fast enough. We can show this by putting 44.1khz white noise through the DAC and observing the output:
It's hardly attenuating anything under 20khz, as we saw earlier, which is great, but it's not attenuating fully until over 26khz, meaning it's not adhering to Nyquist and is not correctly eliminating erroneous imaging. The cursor at 22.05khz (Nyquist frequency) shows that it's basically not attenuating at all there yet.
This DAC does not actually have any filters that correctly adhere to Nyquist theory. But it does have one filter that attenuates a bit steeper called 'apodizing'. Let's look at the filter response for that (I've changed the Y axis scale to dB for this part to make things clearer in the next step).
This one attenuates by 24khz, which is better, though still not correct as by 22.05khz we've only attenuated about 11dB. We can also see that it does this at the expense of rolling off sooner. According to the graph, a 21.5khz signal should be about 5dB lower than a 20khz one, and sure enough:
20khz produces 4.111V.
but 21.5khz produces 2.272V, 5.15dB lower.
Also note that separately from the amplitude thing, the unwanted products above the fundamental are significantly lower than what we saw with the previous filter, at around 10uV instead of 350uV that we saw previously. This is due to the reconstruction filter more accurately eliminating content above Nyquist.
So, the question is then what happens if we use as close to a 'perfect' reconstruction filter as possible?
Well, I'll do this with
PGGB. Same DAC, I'm just upsampling the files to 768khz using PGGB and then feeding that to the DAC rather than just using the DAC's internal reconstruction filter, similar to how the MScaler would. (NOTE: I've set PGGB Gain to -1.0dB for all three files to prevent intersample overs clipping)
Here's 20k:
Here's 21.5k:
So whereas we were getting differences of several decibels with the previous filters, this one we're seeing about 0.02dB even that close to Nyquist. Additionally note that the unwanted distortion product we'd seen above the fundamental previously is completely nonexistant here.
And if we look at the whitenoise test:
About as close to perfect attenuation as we can get.
You can characterize how a filter will attenuate things by looking at the whitenoise response. A 'perfect' filter will do what the graph above shows. Everything below Nyquist left unaltered and everything above it completely attenuated.
Some would argue that a 'sufficient' filter would be one that leaves everything below 20khz unaltered and fully attenuates by 22.05khz, but very few DACs actually manage to even do that anyway. The vast majority of DACs on the market have filters that do not properly reconstruct the signal according to Nyquist theory. Chord's is one of the few that does.
Chord DAVE+MScaler filter response measured at the analog output of the device:
