Schematic

The buffer is connected between C1/C2 and L1 because that seems to give the greatest difference between the outputs (1s and 0s)

I used a buffer to prevent the rectifier from loading the reader

I used a 9V power supply to imitate a 9 volt battery

R12 and R13 are undecided and depend on further study of the rectifier output

I used the LF411 four times because of its ability to handle voltages up to 9V and -9V

I will be using the LM311 for the comparator because of its response time of about 1 microsecond.

The full wave rectifier uses three op amps to create a fast rectifier able to go to 125 KHz. Using Schottky diodes causes one half of the wave to be taller than the other on the output, so I have adjusted two resistors accordingly. (R9: 10K to 11K. R6: 5K to 5.1K)