Example 3.1

 A four-level baseband data stream has a symbol period of 100 ms. 
  1. What is the minimum bandwidth required for transmission, assuming a root raised cosine filter is used with a = 0.3? 
  2. What is the time taken to transmit 1 million bits?
  3. If it is required to transmit the information in half the time, how many symbol states would be required using the same transmission bandwidth?

Solution

  1. The minimum bandwidth required for transmission is half the symbol period for baseband signalling, assuming brick-wall filtering (a = 0). For a = 0.3, this bandwidth must be increased by a factor of (1 + a). Thus for a symbol period of 100 ms, the symbol rate is 10 000 symbols/second, and the bandwidth required is 5000(1 + a) = 65 000 Hz.
  2. With a four-level signalling scheme, there can be two bits encoded in each symbol, hence the bit rate is twice the symbol rate, i.e. 20 kbps. The time taken to send 1 million bits is thus 1 000 000/20 000 = 50 seconds.
  3. To halve the transmission time, we need to encode double the number of bits in each symbol. Thus 4 bits/symbol requires 16 symbol states.