Let continuous-time signals  and  be

Consider the convolution . Then  is

Suppose signal  is obtained by the time-reversal of signal , i.e., . Which one of the following options is always true for the convolution of  and  ?

For the signals  shown in the figure,  is maximum at . Then  in seconds is __________ (Round off to the nearest integer).

Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) * h(t) = y(t). Further, if |x(t)|*|h(t)| = z(t), which of the following statements is true?

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 , and similarly, y(t) is nonzero only for . Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?

Two systems with impulse responses and  are connected in cascade. Then the overall impulse response of the cascaded system is given by

The response h(t) of a linear time invariant system to an impulse , under initially relaxed condition is . The response of this system for a unit step input u(t) is

A Linear Time Invariant system with an impulse response h(t) produces output y(t) when input x(t) is applied. When the input  is applied to a system with impulse response , the output will be

Let s(t) be the step response of a linear system with zero initial conditions; then the response of this system to an input u(t) is

The impulse response of a network is  for  and zero otherwise. Find the impulse response of two such networks in cascade, neglecting loading effects.