Step 1: The Block Diagram

Picture of The Block Diagram
The signal path can be seen in the block diagram above. First, the noise is passed into the mic where it goes to a preamp then an all pass filter to delay the signal.  Finally the noise is input to the summing amp and added to the music signal. This stage also inverts the noise as a summing amplifier is a special case of the standard inverting amp.  The amplitude of the noise is determined by this stage and must be tuned to achieve proper noise cancellation.  The inverted noise plus music signal is then played through the headphones and cancels out the unwanted noise. The next steps explain each stage further.