Chapter 7.5, Problem 30P

Let $g\left(t\right)=u\left(t-\frac{\pi }{k}\right)f\left(t-\frac{\pi }{k}\right)$, where $f\left(t\right)$ is the function of Problem 29 and k > 0. Note that $h\left(t\right)=f\left(t\right)+g\left(t\right)$ is the full-wave rectification of sin ki shown in Fig. 7.5.17. Hence deduce from Problem 29 that ${L}\left\{h\left(t\right)\right\}=\frac{k}{s^2+k^2}\coth \frac{\pi s}{2k}$ .