# What do the frequency components of a fourier transform do to the function itself?

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.

• You may want to check out the Riemann Lebesgue Lemma and its proof. Basically, you use integration by parts to translate statements about decay of fourier coefficients to statements about $f$'s derivatives. – SquirtleSquad Mar 17 '17 at 1:33
• Here's an example of the technique I described: math.stackexchange.com/questions/2090803/… – SquirtleSquad Mar 17 '17 at 1:36