An exact solution for a notch filter transfer function using an operator formalism

The transfer function for a notch filter is calculated. Matrix operators are used extensively to track the dual frequencies generated in the feedback loop. The final result includes contributions from both the sum and difference frequencies. To obtain the exact solution it is necessary to represent the problem in an operator formalism. This matrix representation allows the frequency shifting of the demodulator and remodulator to be easily accommodated. The inverse operator needed for the proper representation of the feedback loop is easy to perform in a matrix representation