Let $$m\left(t\right)\;=\cos\left[\left(4\mathrm\pi\times10^3\right)t\right]$$ be the message signal and $$c\left(t\right)\;=5\cos\left[2\mathrm\pi\times10^6t\right]$$ be the carrier.

c(t) and m(t) are used to generate an AM signal. The modulation index of the generated AM signal is 0.5. Then the quantity $$\frac{Total\;sideband\;power}{Carrier\;power}$$ is

A DSB-SC signal is to be generated with a carrier frequency f_c = 1MHz using a nonlinear device with the input-output characteristic $$v_0=a_0v_i\;+\;a_1v_i^3$$.where a₀ and a₁ are constants. The output of the nonlinear device can be filtered by an appropriate band-pass filter. Let $$v_0=A_c'\;\cos\left(2{\mathrm{πf}}_\mathrm c'\mathrm t\right)\;+\;m\left(t\right)$$ where m(t) is the message signal. Then the value of $$f_c'$$ (in MHz) is

The signal flow graph of a system is shown in figure. The transfer function $$\frac{C(s)}{R(s)}$$ of the system is

Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t-2). The transfer function of the system should be