A digital communication channel is capable of transmitting 56600 bits per second, about the rate of a high-speed dial-up modem at the turn of the century. We want to use this channel to transmit a...

A digital communication channel is capable of transmitting 56600 bits per second, about the rate of a high-speed dial-up modem at the turn of the century. We want to use this channel to transmit a single analog signal x(t) with lowpass content. The signal magnitude is limited to |x(t)| ≤ xmax. System specifications require that the error between the digitized signal and x(t) must not exceed ±10⁻³x_max.

(a) What is the required number of bits B of the ADC?

(b) What is the maximum bandwidth of the analog input for which the channel can be reliably used without aliasing errors?

(c) Suppose that our desired message x(t) is streamed audio, which has a maximum frequency content of around 3500 Hz. Will the system work? If yes, justify how. If not, explain what you might do to best accommodate this particular message signal so that the channel can be used.