How do you interpolate FFT?
The fastest way to compute a single interpolated FFT spectral sample at frequency k is to merely compute a brute force N‑point DFT of the original x(n) time samples using: where, again, 0 ≤ k ≤ N‑1, and k is not an integer. Assuming the x(n) input in Eq. (6) is real-only, the computational workload comparison of Eq.
How do you interpolate two functions?
The simplest function is to find the closest points and use linear interpolation. e.g. chose two of three closest points and interpolate them. Or you can take a weighted average based on distance. Or you can pick a close point and then find points on the "other side" of the closest point to improve the interpolation.