The causal signal with $z$-transform $z^2(z-a)^{-2}$ is ( $u[n]$ is the unit step signal)

Let $f(t)$ be an even function, i.e., $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as

$F(\omega)=\int_{-\infty}^{\infty} f(t) e^{-j \omega t} d t$. Suppose $\frac{d F(\omega)}{d \omega}=-\omega F(\omega)$ for all $\omega$ and $F(0)=1$. Then

If the input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\max [0, x(t)]$, then the system is