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 system described by the differential equation: $${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dt}} + 2y = x(t)$$ is initially at rest. For input x(t) = 2u(t), the output y(t) is

The z transform of a system is
H(z) = $${z \over {z - 0.2}}$$ .
If the ROC is $$\left| {z\,} \right|$$ < 0.2, then the impulse response of the system is

The Fourier transform of a conjugate symmetric function is always