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

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

A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.

Assuming the signal to be uniformly distributed between its peak values, the signal to noise ratio at the quantizer output is