Best Demodulator

• If we compute averages of the received signal over each bit period we obtain:
  
  $$-0.0129 \; 0.0432 \; 0.2212 \; 0.2590 \; -0.4309 \; 0.4349 \; -0.0585 \; 0.2158 \; -0.7929 \; 0.0709$$
  
  

• Decisions might be formed as before: positive average implies ``1'', negative average implies ``0''.
• Notice, that many wrong decisons result.
• Also, the above averages are near zero.
• This is because the average of the pulses is equal to zero.
• To improve we must use weighted averages.
• The weighting is proportional to the amplitude of the pulses.
• In this example, the received signal must be weighted (multiplied) by +1 i n the first half of the bit period and by -1 in the second half of the bit period.
• The properly weighted received signal is shown in Figure 2.35.
• The weighted averages for the ten bit periods are:
  
  $$0.4038 \; 0.9521 \; -1.0175 \; 0.8610 \; -1.1932 \; -0.8561 \; 0.4753 \; -1.0229 \; -0.8380 \; -1.1493$$
  
  

• All decisions are correct!

  

Figure 2.35: Weighted Received Signal.