The Heisenberg uncertainty principle applies here… you cannot make a measurement which is both precise in frequency and compact in time.
This should be, in some sense, natural to people who understand how a Fourier transform works… basically, when you apply a “window” function to measure a signal over a limited period of time, you end up with the signal smeared in the frequency domain.
This should be, in some sense, natural to people who understand how a Fourier transform works… basically, when you apply a “window” function to measure a signal over a limited period of time, you end up with the signal smeared in the frequency domain.