I have several signals, that I am trying to find a metric to compare the signal smoothness. By signal smoothness I mean, the signal that the distance between the peak to trough become smaller (getting close to becoming flat) is smoother, and if this peak-tough distance increases it becomes wavier.
I can fit a Fourier series with eight terms to all of them. it means that I do have a Fourier series equation with eight terms for all of them.
My question is that how I can compare the Fourier series coefficient to each other, in order to evaluate the signal smoothness?
since for a single term Fourier series (i.e f(x)=a0+a1cos(xw)+b1sin (xw)) I can use the "sqrt ((a1^2)+(b1^2))" as an indicator of surface smoothness. but I do not know what I should do when it has eight terms? Thank you