Originally Posted by davek
I may be completely wrong, but I don't understand how a 16k point DFT can measure the frequency of maxplanck's test tone beyond a precision of +/- about 3 Hz -- unless I'm missing something.
Well first, for his test tone, the best resolution a 16k DFT can give you is 0.12Hz, not 3Hz (formula is 2*bandwidth/bins).
What I said before was that at 48kHz you got 3Hz, but it depends on the sample rate you choose. I picked 48kHz because its a common value. Its actually not a very good value to choose since the test tone is only 1kHz.
More broadly speaking, you need to consider that the clock probably isn't stable to fractions of a Hz. It probably has a fairly wide fractional bandwidth, just because its a low power, low cost device. You just want to measure it to one part in a hundred or so. Any reasonable sized transform can do that.