I thought for a while intuitively about the relationship between the frequencies in the fourier transform of a function and the function itself.
After a while, I figured out that higher frequencies cause a function to be "jumpier" and less smooth. Is this interpretation true?
Do the frequencies in the fourier representation of a function represent the "smoothness" of the function in time domain? This would explain why many functions, when you cutoff their high frequency components, become smoother.