A rectangular pulse train s(t) as shown in Fig.1 is convolved with the signal $${\cos ^2}$$ ($$4\pi \,{10^{3\,}}$$t). The convolved signal will be a

A causal system having the transfer function H(s) = $${1 \over {s + 2}}$$, is excited with 10 u(t). The time at which the output reaches 99% of its steady state value is

Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in Fig.(1) & (2).

Then Y(f) is

The impulse response $$h\left[ n \right]$$ of a linear time-invariant system is given by $$h\left[ n \right]$$ $$ = u\left[ {n + 3} \right] + u\left[ {n - 2} \right] - 2\,u\left[ {n - 7} \right],$$ where $$u\left[ n \right]$$ is the unit step sequence. The above system is