No, I don't assume 44.1KHz captures perfectly upto 20KHz,  I know it DOES.

Here is an intresting web pages that demonstrates this:-

http://www2.egr.uh.edu/~glover/applets/Sampling/Sampling.html

It is showing that there is absolutely no point in sampling more than twice the required frequency, that was discovered in 1928 and proved in 1959.

You must never overlook the fact that human beings cannot hear anything above 22KHz (most people struggle above 18KHz), so any harmonics above that will never be heard and thus there is no point in capturing them.

Actually, have you realised that any fundamental waveform above 10KHz will sound like a sine wave to us?  Because the second harmonic is beyond what we can hear.

@andyjh said:

 No, I don't assume 44.1KHz captures perfectly upto 20KHz,  I know it DOES.

Here is an intresting web pages that demonstrates this:-

http://www2.egr.uh.edu/~glover/applets/Sampling/Sampling.html

It is showing that there is absolutely no point in sampling more than twice the required frequency, that was discovered in 1928 and proved in 1959.

You must never overlook the fact that human beings cannot hear anything above 22KHz (most people struggle above 18KHz), so any harmonics above that will never be heard and thus there is no point in capturing them.

Actually, have you realised that any fundamental waveform above 10KHz will sound like a sine wave to us?  Because the second harmonic is beyond what we can hear.

 The half frequency theory (Nyquist) does state that it assumes a perfect bandwidth limit (a theoritcal brick wall filter - which does not seem possible),  and there is a slight "grey" area when it comes to exactly half the frequency (that would be 22.05 KHz sampling at 44.1KHz).  So this is why the frequency response of a sampling frequency is always less than half, to allow for a real world filter.

You must not allow anything over half the sampling frequency to be sampled, because it will alias, and you cannot sort out aliasing on playback, because the frequencies have already been "folded back" are then part of the sub 20KHz signal.

It is how good this filter is, that determines the quality of an A/D conversion, if the filter is weak it may allow aliasing to happen, if it is over zealous, it will start to affect audible frequencies that it should not be affecting.  A good quality filter design will perfectly deal with the critical 22Khz frequency, yet be perfectly out at 20KHz.  But - some converters will be struggling.  If you shift the sampling to 96KHz, you can put a very lazy filter in there that easily kills any aliasing, and does not affect sub 20KHz frequencies.  So it's a lot easier to make a perfect 96KHz sampling frequency than it is a 44.1KHz one. Which is why some audio interfaces "seem" to sound better at 96KHz.

It is however better to buy a top quality audio interface and run at 44.1KHz (or 48KHz if your output medium requires it), than invest in a super fast computer that has to deal with 96KHz sampling.  The end result wil be the same. Especially as the final product is unlikely to be at 96KHz anyway.

@andyjh said:

 The half frequency theory (Nyquist) does state that it assumes a perfect bandwidth limit (a theoritcal brick wall filter - which does not seem possible),  and there is a slight "grey" area when it comes to exactly half the frequency (that would be 22.05 KHz sampling at 44.1KHz).  So this is why the frequency response of a sampling frequency is always less than half, to allow for a real world filter.

You must not allow anything over half the sampling frequency to be sampled, because it will alias, and you cannot sort out aliasing on playback, because the frequencies have already been "folded back" are then part of the sub 20KHz signal.

It is how good this filter is, that determines the quality of an A/D conversion, if the filter is weak it may allow aliasing to happen, if it is over zealous, it will start to affect audible frequencies that it should not be affecting.  A good quality filter design will perfectly deal with the critical 22Khz frequency, yet be perfectly out at 20KHz.  But - some converters will be struggling.  If you shift the sampling to 96KHz, you can put a very lazy filter in there that easily kills any aliasing, and does not affect sub 20KHz frequencies.  So it's a lot easier to make a perfect 96KHz sampling frequency than it is a 44.1KHz one. Which is why some audio interfaces "seem" to sound better at 96KHz.

It is however better to buy a top quality audio interface and run at 44.1KHz (or 48KHz if your output medium requires it), than invest in a super fast computer that has to deal with 96KHz sampling.  The end result wil be the same. Especially as the final product is unlikely to be at 96KHz anyway.

@gregb said:

---- You have not explained fig 8. i.e. more than 2 signals both sharing the same sampling points but both below nyquist/2..... according to you this error should not exist.

Fig 8 is showing 3 sines at the same frequency, but phase shifted by +/- 90 degrees and at the critical frequency (which is half the sampling frequency), which is why I suggested "half" the frequency is a grey area, because it needs to be just under half (-1Hz). An audio waveshape would not look like this, it would be one composite wave shape, but we do need to describe things in terms of sine waves as that is how the maths works.

I guess the required sampling frequency should be described as double plus 1Hz,  though at 44.1KHz we are already double plus 2050Hz - which well clears the critical frequency.  Aliasing filters is the enemy not the critical frequency.