This question asks what's the point of zero padding. The accepted answer is certainly very insightful, but I don't understand a big chunk of it:
Zero padding allows one to use a longer FFT, which will produce a longer FFT result vector.
A longer FFT result has more frequency bins that are more closely spaced in frequency. But they will be essentially providing the same result as a high quality Sinc interpolation of a shorter non-zero-padded FFT of the original data.
This might result in a smoother looking spectrum when plotted without further interpolation.
Although this interpolation won't help with resolving or the resolution of and/or between adjacent or nearby frequencies, it might make it easier to visually resolve the peak of a single isolated frequency that does not have any significant adjacent signals or noise in the spectrum. Statistically, the higher density of FFT result bins will probably make it more likely that the peak magnitude bin is closer to the frequency of a random isolated input frequency sinusoid, and without further interpolation (parabolic, et.al.).
What exactly is the meaning of "resolve" and "resolution" here, and how, mathematically, is it apparent that zero padding does not increase resolution. Dually, how is apparent mathematically that zero padding means interpolation?