A$.$ Let a message with sine wave $x(t)$ be the input to $DM,$ where $x(t)$ is given by $x(t)=10si{n}^2(2{10}^{3}t)+20sin(2{10}^{3}t)+4sin(2{10}^{3}t)$

Determine the minimum value of step size that will prevent slope overload, if the message is sampled by using Nyquist rate.

B$.$ Draw the Frequency division multiplexing and frequency division DE multiplexing for $12$ single side signal with each frequency $2KHz,$ and carrier frequency $100KHz,$ then determine the time constant for the receiver if we used to envelop detector and DE multiplexer.

An FM signal with modulation index $=4$ is transmitted through an ideal band$-$pass

C$.$ filter with midband frequency $f_{,}$ and bandwidth $7,$dots, where $f,$ is the carrier frequency and $f_m$ is the frequency of the sinusoidal modulating wave. Determine the magnitude spectum of the filter output.