Look at the images below. The first is time signal, the second is
corresponding amplitude spectrum.
There are 64 values in the sampled time signal.
Corresponding 32 amplitude values of the signal spectrum are shown on
another figure, and - oh, that's a surprise! - none-zero frequency component
is found in the 5th value, and 5 is 4 plus 1. That's why it's convenient to
use zero-based arrays. Then we would call the value 4th, not 5th.
Then resolution is 44100 / 64 = 689 Hz, and the sine wave frequency
is 4 * 689 = 2756 Hz.
Assume the sampling frequency is 44100.
Then the signal duration is 64 / 44100 = 0,00141 sec.
It would be exactly 1 sec if we had 44100 samples - but we only have 64.
The signal consists of constant component and a sine wave. It
is also important to note that exactly 4 periods of sine wave fit in the
time signal being analysed.