"capturing the frequency domain information at 20KHz, 44.1KHz sampling is completely sufficient to perfectly capture the sine waves"
Maybe sufficient for sinewaves but not for the music because it would call for brick wall filters that have very uneven group delays (non-linear phase if you prefer) and will cause wrong summing of harmonics. Such setup will be OK for single frequency reproduction but will be very unpleasant with music (dynamic signal).
Yes it is coarse because Nyquist-Shannon theorem requires infinite amount of terms (samples). Fixing it with sin(x)/x works poorly for short bursts around 1/2 of the sampling frequency. Sound of instruments producing continuous sound might be not affected (like flute) but anything with transients will sound wrong (piano, percussion instr. etc). Notice, that when people compare analog to 16/44 first thing they notice is different sound of the cymbals.
On the other hand, if you still think it is perfect system - enjoy.
Maybe sufficient for sinewaves but not for the music because it would call for brick wall filters that have very uneven group delays (non-linear phase if you prefer) and will cause wrong summing of harmonics. Such setup will be OK for single frequency reproduction but will be very unpleasant with music (dynamic signal).
Yes it is coarse because Nyquist-Shannon theorem requires infinite amount of terms (samples). Fixing it with sin(x)/x works poorly for short bursts around 1/2 of the sampling frequency. Sound of instruments producing continuous sound might be not affected (like flute) but anything with transients will sound wrong (piano, percussion instr. etc). Notice, that when people compare analog to 16/44 first thing they notice is different sound of the cymbals.
On the other hand, if you still think it is perfect system - enjoy.