# Spectral Content of two waveforms

I have found this interesting question here:

Which of these two waveforms has a richer spectral content, and why?

Intuitively speaking, I think that the first one is richer, but I cant really justify it! Cheers for any input.

Your intuition is correct. The reason is that the rectangular pulse train has discontinuities, whereas the rectified sine is continuous (but its derivative has discontinuities). The consequence of this is that the Fourier coefficients of the rectangular pulse train decay as $1/n$, whereas the coefficients of the rectified sine decay as $1/n^2$ (where $n$ is the index of the Fourier coefficients).