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
