If our sample size, , is not large enough, we might experience time domain aliasing. The figures under shows this very clearly, and as gets small, we can not recover the original signal anymore.
Using samples is called Zero Padding , and improves resolution.
Zero Padding
We add zeroes at the end of our signals before we DFT - Discrete Fourier Transform to get more sticks, and therefore higher resolution.
Link to original
In frequency domain
In time domain (Figure 3)
