Has anyone ever thought about non-uniform sampling? Forget the obvious hardware problems and think about it mathematically. Sampling is used as a spectral estimation process, however if you note the Nyquist-Shannon theorem you'll see that the sampling time-width (the time you sample over) is allowed to go to infinity. Allowing the timewidth to go to infinity asymptotically drives the spectral estimation error to zero. However, if we limit the timewidth to T, and uniform sample, our estimation is inherently biased to multiples of the sampling frequency, but not samples in between, DPS guys will say that the timewidth T sets the frequency resolution.
So, what if we non-uniformly sample? What is the best way to do so? What I mean by this is if I'm going to take N samples over a timewidth T where is the best place to take my samples? I would bet its non-uniformly. The only thing that our good friend Nyquist demands is that two samples be spaced close enough so that we don't alias, but he says nothing about how this is to be achieved.
I think uniform sampling is very easy and obviously works well, but I've not seen much work done where we ask ourselves if uniform sampling is really the best way to estimate a spectrum.
So, what if we non-uniformly sample? What is the best way to do so? What I mean by this is if I'm going to take N samples over a timewidth T where is the best place to take my samples? I would bet its non-uniformly. The only thing that our good friend Nyquist demands is that two samples be spaced close enough so that we don't alias, but he says nothing about how this is to be achieved.
I think uniform sampling is very easy and obviously works well, but I've not seen much work done where we ask ourselves if uniform sampling is really the best way to estimate a spectrum.