Four messages band limited to W, W, 2 W and 3 W respectively are to be multiplexed using Time Division Multiplexing (TDM). The minimum bandwidth required for transmission of this TDM signal is

Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-dB cut-off frequency of f_c. The noise power at the filter output is

The signal $$\cos\;\omega_ct\;+\;0.5\;\cos\;\omega_mt\;s\mathrm{in}\;\omega_ct$$ is

Consider the amplitude modulated (AM) signal $$A_c\cos\omega_ct\;+\;2\cos\omega_mt\;\cos\omega_ct$$. For demodulating the signal using envelope detector, the minimum value of A_c should be