The impulse response g(t) of a system G, is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of G as shown in Figure (b)?

The signum function is given by $$$\mathrm{sgn}\left(\mathrm x\right)=\left\{\begin{array}{l}\frac{\mathrm x}{\left|\mathrm x\right|};\;\mathrm x\neq0\\0\;;\;\;\mathrm x=0\end{array}\right.$$$ The Fourier series expansion of sgn(cos(t)) has

Consider a discrete time signal given by
x[n]=(-0.25)ⁿu[n]+(0.5)ⁿu[-n-1]
The region of convergence of its Z-transform would be