Consider the design of a digital communication system to carry the music and voice signals that are currently broadcast by FM radio stations. This is an example of digital audio broadcasting (DAB) system. In your design, you need to choose values for all system parameters, using your judgement to include "error margins" so that the system can be implemented with reasonable cost.

The analog signal characteristics are as follows. These will help you design the PCM subsystem.

• Bandwidth = 15 kHz
• The signal-to-noise ratio (SNR) of the analog signal at the receiver should be approximately 50 dB.

Some other information about the system is as follows.

• The channel that will transmit the PCM data is characterized by a SNR of 20 dB or 100. This is the SNR that enters Shannon's formula for channel capacity, C = W log₂ ( 1 + SNR ) bps, where W is the channel bandwidth in Hz.
• The system must be simple and low-cost, so no channel coding (error correction coding) will be included.

1. For the PCM subsystem, what is the sampling rate? How many bits are used to represent each sample?
2. What bandwidth is required for the channel? How many bits will each pulse carry across the channel? What reasoning did you use to decide the number of bits/pulse? What shape did you choose for the pulses? Why?
3. What are some possible approaches to reducing the required channel bandwidth? What are the tradeoffs involved in the various approaches? Why might it be desirable to reduce the channel bandwidth?