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.
-- FAReceived on Sat Jan 28 04:15:15 2006
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