Say that I have a continuous signal. If I sample the signal at sampling rate f_sample
, then the highest signal frequency that I can resolve without worrying about aliasing, etc. is the Nyquist rate f_Nyquist = 0.5 * f_sample
, so arguably I could interpret this as meaning that the time resolution of my signal is dt_min = 1 / f_Nyquist = 2 / f_sample
. Fine.
However, the above is for instantaneous sampling. How does the picture change if each of my samples involves averaging over a given finite time period t_width
, with the possibility that successive time periods overlap by a time t_overlap
? (See picture. Equation for t_overlap
in the picture ignores cases where overlap extends beyond that of nearest neighbors, but it's easy to generalize.)
I.e., in the case that t_width = t_overlap = 0
, I have f_Nyquist = 0.5 * f_sample
, dt_min = 2 / f_sample
, as above. For the case that t_width, t_overlap != 0
, is there still a simple statement that I can make regarding f_Nyquist
, or more importantly some generalization of f_Nyquist
which is relevant to the quantity that I am actually interested in, namely the time resolution of my signal t_min
? Is there a simple equation for something that is interpretable as t_min
that could be used in such a situation?
Extra:
The above is the main thing I am interested in. However, just to add one more generalization in case anyone happens to know it: If the averaging weight function over t_width
is not uniform, but is instead something more complicated (e.g., Gaussian), is there still a relationship or theorem that can help me figure out what t_min
is?
Thanks for any help!
P.S.
If my interpretation of the Nyquist rate is wrong or anything, let me know and I'll correct it in the post.
I think this is the right StackExchange site for this question, but if there is another that anyone knows of where an answer is more likely, please suggest it.