Interpolation estimates an unknown value between two known points by assuming how the quantity behaves in between — the simplest assumption being a straight line.
Smoothing deliberately misses your points instead of passing through them, trading some bias for a lot less noise - and every method on this page is just a different opinion about how to make that trade.
The Fourier transform turns samples over time into amplitudes over frequency - the DFT defines it, the FFT computes the same numbers fast.
The inverse Fourier transform turns amplitudes over frequency back into samples over time - the IDFT defines it, the IFFT computes the same numbers fast.
Detrending subtracts the slow baseline under your data so that peaks and oscillations are read from a flat zero - and the method you choose decides how much of the signal survives.
A digital filter is designed in hertz, not in points: you choose which frequencies stay, and its frequency response tells you exactly what happens to the rest.
Cross-correlation is Pearson's r computed again at every time shift: the shift with the highest r is the delay between two signals, and in a signal against itself the first peak is its period.
An outlier is judged against a center and a spread - and because the mean and the standard deviation are pulled by the outlier itself, robust ones (median, MAD, quartiles) find what the z-score misses.
A fit is a model, not a curve through your points: least squares picks the few coefficients that make the vertical misses smallest, and the residuals left over tell you whether the model was the right one.
One number per pair, from −1 to 1: how tightly two columns follow a straight line, which a perfect curve can still score zero on, and which never says what causes what.
A local maximum is one line of code; deciding which bumps count, and splitting peaks that overlap into their true width, height and area, is the whole job.