A method of measuring beat frequency comprises modulating a first optical signal and a second optical signal, wherein the first modulated optical signal includes a first carrier frequency and a first plurality of sideband frequencies and the second modulated optical signal includes a second carrier frequency and a second plurality of sideband frequencies. The method also comprises combining a fraction of the first modulated optical signal with a fraction of the second modulated optical signal into a combined signal and determining a carrier beat frequency. The method further comprises selecting a frequency range from the combined signal; performing a fast Fourier transform (FFT) on an electrical signal representing the selected frequency range; tracking the carrier beat frequency based on the FFT; and outputting a rate signal based on the tracked carrier beat frequency, the rate signal indicating a rotation rate of the resonator fiber optic gyroscope.