The Nyquist theorem states that the sampling rate must be twice the highest frequency to be observed. How does the length of the interval play into this relationship?
The main resource that I found here states that
For a waveform to be fully characterized, it must complete at least one full cycle within the duration of the time record.
Is this the only restriction, assuming that my sampling rate exceeds the Nyquist rate? For example, assume that the frequency band I wish to measure is from 8Hz to 13Hz. I have a sampling rate of 2000 Hz, which is way beyond the Nyquist frequency. As long as my time window is at least 1000ms / 8 Hz = 125 ms, should I be able to reconstruct the signal? For context, I am planning on running an FIR filter followed by a Hilbert transform on these windows to extract phase information, so I want the analytic signal to be mathematically sound.