How to determine Nyquist Rate
For finite length or time limited signals, the Nyquist rate only makes sense given some finite noise floor requirement and finite total signal energy.  You look for the frequency at or above which nothing is above that noise floor and the total remaining energy is below that noise floor.  Twice that is the minimum sampling frequency to avoid aliasing causing any noise above that given floor.

For infinite length signals, there is the possibility of a frequency domain window of finite support width.