Hi Aaron,
aaron_do wrote on Jul 23rd, 2013, 5:22pm:I have slept on it, and I think that maybe your explanation may be correct. My apologies. Im still not sure whether it tells the full story though. My concern is what if you have a real signal which is changing. It is not the same as having a limited number of samples, so if you convert to the frequency domain, with more samples the spreading will be less. But for some parts of the signal you may encounter the problem...
I don't think so. All samples of the signal contribute to every frequency component. The influence of the sampling error of every single sample does not depend on the level of the signal at that instant because the Fourier transform is linear.
Assuming white noise (with its flat power spectral density), the SNR of a certain frequency component depends directly on the power of that component (to which all samples contribute).
This is applies at least to the case of a band-limited signal of which you have all (infinitely many) samples.
I'm not sure whether that covers the case you think of, though.
- B O E