A DSB-SC signal is generated using the carrier $$\cos\left(\omega_ct\;+\;\theta\right)$$ and modulating singal x(t). The envelope of the DSB-SC signal is

The image channel selectivity of super heterodyne receiver depends upon

The number of roots of $$s^3\;+\;5s^2\;+\;7s\;+\;3\;=\;0$$ in the left half of the s-plane are

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation e^-at u(t), a > 0 will be