Let a frequency modulated (FM) signal $$x(t) = A\cos ({\omega _c}t + {k_f}\int_{ - \infty }^t {m(\lambda )d\lambda )} $$, where $$m(t)$$ is a message signal of bandwidth W. It is passed through a non-linear system with output $$y(t) = 2x(t) + 5{(x(t))^2}$$. Let $${B^T}$$ denote the FM bandwidth. The minimum value of $${\omega _c}$$ required to recover $$x(t)$$ from $$y(t)$$ is

Let x$$_1$$(t) and x$$_2$$(t) be two band-limited signals having bandwidth $$B=4\pi\times10^3$$ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is

Consider an FM broadcast that employs the pre-emphasis filter with frequency response

$${H_{pe}}(\omega ) = 1 + {{j\omega } \over {{\omega _0}}}$$,

For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pairs of (R, C) values is/are ____________.