"I can kind of picture the fourier transform meaning that there's only one representation but it's a bit of a leap for me.Can the converter itself not create the signal incorrectly?"
Well. the converter add always small amounts of noise into the signal that could accumulate to 1 less significant bit or more.
With some special signals, mostly those made by man, like radar or sonar you could add more error(as signal accumulates so much in selected frequencies with exact multiples that have a strong bias) but most natural audio signals don't have much trouble.
"Isn't there also an argument that frequencies above 19khz can be heard by some people so need to be accurately represented?"
No, most kids could hear above 19khz, most adults can't, no argument about that, it is something you could test with a speaker and an electronic workbench using your kids or family members.
Nyquist proved that if you have a SAMPLED signal, with the FT you could reconstruct EXACTLY the same sampled signal, provided that you don't add quantization errors and so, that are small, you could even reconstruct square signals(with signal in all frequencies).
In the case you see those differences you will hear those transformation errors if they were significant(they are not), or you will have to turn on the volume and will hear a "sssssshhhhhhhhhh" sound.
Well. the converter add always small amounts of noise into the signal that could accumulate to 1 less significant bit or more.
With some special signals, mostly those made by man, like radar or sonar you could add more error(as signal accumulates so much in selected frequencies with exact multiples that have a strong bias) but most natural audio signals don't have much trouble.
"Isn't there also an argument that frequencies above 19khz can be heard by some people so need to be accurately represented?"
No, most kids could hear above 19khz, most adults can't, no argument about that, it is something you could test with a speaker and an electronic workbench using your kids or family members.
Nyquist proved that if you have a SAMPLED signal, with the FT you could reconstruct EXACTLY the same sampled signal, provided that you don't add quantization errors and so, that are small, you could even reconstruct square signals(with signal in all frequencies).
In the case you see those differences you will hear those transformation errors if they were significant(they are not), or you will have to turn on the volume and will hear a "sssssshhhhhhhhhh" sound.