Consider a periodic square wave $f(t)$ with a period of $1$ second such that $f(t)=1$ for $t \in[0,1 / 2)$ and $f(t)=-1$ for $t \in[1 / 2,1)$. It is passed through an ideal low-pass filter with cutoff at $2 \mathrm{~Hz}$. Then the output is
- $\sin (2 \pi t)$
- $\cos (2 \pi t)$
- $\sin (2 \pi t)-\sin (6 \pi t) / 3+\sin (10 \pi t) / 5-\ldots$
- $\sin (2 \pi t)-\cos (2 \pi t)$
- None of the above