I have a periodic function $\sigma(x)=\sigma(x+R)$ of period $R$ specified by:
\begin{equation} \sigma(x)=\begin{cases} \sigma_1, \quad 0\leq x\leq d \\ \sigma_2, \quad d\leq x\leq R \end{cases} \end{equation}
over a period. There is a step-discontinuity at $x=d$, and it is like a square wave, but the two fixed values are $\sigma_1$, $\sigma_2$ rather than $\pm 1$, and the duty cycle is not $0.5$.
Is there a way to write this function in a form $\sigma(x)=\sigma_0 s(x)$, where $s(x)$ is a periodic function given in analytical form?