Harmonic power of a square wave ($P_{\{r,-r\}}/P=8/({\pi }^2{r}^2),r\text{ odd}$)

A zero-mean square wave of amplitude $G$ has total mean-square signal power $G^2$. Each positive odd Fourier harmonic and its negative-frequency partner contribute $8G^2/({\pi }^2{r}^2)$, by its exact Fourier coefficients. The fundamental pair therefore accounts for $8/{\pi }^2$ of the total. The sum of contributions above harmonic index $R$ decays on the order of $R^{-1}$, although the discontinuous waveform still requires arbitrarily high harmonics for exact reconstruction.