27 Jan
2006
27 Jan
'06
8:15 p.m.
On Sat, Jan 28, 2006 at 01:30:54AM +0100, Esben Stien wrote:
So this argument with only a few samples on the high
frequencies is
not holding up.
Exactly. And it's quite easy to see why this is true.
Imagine the sample frequency is Fs and you have perfectly sampled a
sinewave with frequency f (or calculated the samples). The inverse of
sampling consist of creating an analog signal wherein each sample
becomes a very thin 'spike' with the sample's amplitude, and that
is zero in between those pulses. (*)
If you calculate the spectrum of that signal, you find it contains
all frequencies of the form k * Fs +/- f, with k and integer. To
reconstruct the sine, you need to filter all of them out except the
original f (and -f). Now this becomes more difficult as f approaches
Fs / 2, as in that case Fs - f will be quite close to f, ** but it is
nevertheless just a matter of filtering and of nothing else **.
One big reason for going up to 96kHz is not primarily
because of being
able to sample high frequencies, but because you don't need such a
sharp filter at the input that may taint your input signal.
Again very true. The main reason why some people can hear a very very
subtle difference between 48 and 96 kHz seems to be that it's quite
difficult to make a 'perfect' filter for 48 kHz, even digitally. There
are very few DACs that get this right (e.g. Apogee, and you pay for it).
(*) Of course most DACs will 'hold' the value until the next sample
time, giving a 'staircase' waveform rather than pulses, but that
doesn't change anything fundamentally.
--
FA