When the sampling rate is T, the resolution is 2T by Nyquist theorem. Maybe irregular sampling can do it. I want some details about irregular sampling.
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without additional knowledge on the signal, you will not beat Nyquist even with non-uniform sampling :
https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem
(see non-uniform sampling section)
now, if you have additional information on your signal, things can be dramatically different
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see "compressed sensing" in the case of sparse spectrum signals, for instance.
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see also (for multiband signals) :
http://webee.technion.ac.il/people/YoninaEldar/Download/76j.pdf
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Dear Zhihua,
I am not sure the question as posed is clear enough. However, I will try. There is not a lot of literature on irregular sampling at high frequencies because it can be intractable. I think that a typical approach (search on unequally spaced FFT) is to do a spline interpolation over the available data, resample and then take a DFT from that. Personally this does not respect the uncertainties from the interpolation.
First of all, it had better be the case that you are trying to capture a periodic stationary signal or the above method will be a disaster. Second, the errors of estimation will not be the same for each frequency, which may be a disaster for your interest in capturing a higher frequency.
i think it might be more promising to adapt a wavelet method but it would be critical to know more about what you are trying to capture to make this worthwhile.
Finally, for rate T, resolution is 1/2 T, not 2T...
Good Luck.
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