Consider the system as shown below:

where y(t) = x(e^t). The system is

Consider a continuous-time system with input x(t) and output y(t) given by $$y\left(t\right)=x\left(t\right)\cos\left(t\right)$$. This system is

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)?

x(t) is nonzero only for $$T_x\;<\;t\;<\;T_x^1$$ , and similarly, y(t) is nonzero only for $$T_y\;<\;t\;<\;T_y^1$$ . Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?