Now my question: Why, oh why, does Audacity, foobar2000, WMP et al play this back with beats? There is a .5sec periodic amplitude osc going on.
Is there a common transition band specified by Red Book CD Audio or other standards to which DAC devices must / should adhere?
Even SoX, regarded as a high-quality tool for this kind of manipulations, states in it's manual "note that band-width values greater than 99% are not recommended for normal use as they can cause excessive transient echo". SoX' default is 95%.
When I generate a clean 3999 Hz tone sampled at 8000 Hz quantized to 16 bits with dither and play it back in foobar2000 using the SoX resampler plugin (95% passband, min phase, best quality, no aliasing) I can hear nothing.
For better or for worse, SoX works to the 3dB point; so by default, you're 3dB down at 95%. With SoX, the corresponding 0dB point is at 91.x% ...
Edit: Indeed, the beating is also present if you create a 23999- or 22049-Hz tone at 48 or 44.1 kHz sample rate, respectively, so it has nothing to do with upsampling. And the frequency of the tone is correct in both cases, I checked with Audition. So what's the explanation? Intermodulation distortion between tone and sampling frequency?
...so long as the rest of the process up to the sound waves reaching the listener's ear is linear, or are you suggesting that a 23kHz tone and a 25kHz tone with a 48kHz sample rate cannot create a 2kHz tone?
What I find curious is that I see the beating in Adobe Audition where I had assumed it could display what the waveform would look like with perfect reconstruction. Clearly I don't understand how the program is going about connecting the dots.
sox -r 8000 -n 1.wav synth 8 sine 3990 gain -1
sox 1.wav 2.wav rate -b 99.7 44100
sox -r 44100 -n 3.wav synth 8 sine 3990 gain -1
sox -M 2.wav 3.wav 4.wav gain -e
Aliasing is nonlinear distortion so I don't see what's confusing about saying distortion is likely when resampling tones very close to Nyquist.
Because its being resampled to 48k, and there is generally massive distortion of anything with 1% of the Nyquist limit with even very high quality resamplers. Theres a reason 44.1khz audio is 4.1khz above the highest frequency humans are expected to hear.