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

Two discrete-time linear time-invariant systems with impulse responses $h_1\lfloor n\rfloor=\delta\lfloor n-1\rfloor+\delta\lfloor n+1\rfloor$ and $h_2[n]=\delta[n]+\delta[n-1]$ are connected in cascade. Where $\delta[n]$ in the Kronecker delta. The impulse response of the cascade system