# 4.1 $U[x]=-1+\theta[x+1]+\theta[x-1]$

The Fourier series representation of $U[x]$ is illustrated below. The three plots below illustrate the evaluation frequencies $f=1$, $f=2$, and $f=3$ respectively and include the left-half plane as well as the right-half plane. Note$U[0]=0$ and $U[x]$ is an odd function of $x$ (i.e. $U[-x]=-U[x]$).