A system is provided that includes a mechanical resonator, and an analog circuit coupled to the mechanical resonator. The analog circuit is arranged to receive a mechanical resonator measurement signal having a quadrature error from the mechanical resonator, and to extract a quadrature error signal from the mechanical resonator measurement signal using a quadrature clock. A digital quadrature controller is coupled to the analog circuit and is arranged to generate a quadrature error compensation signal from the extracted quadrature error signal and apply the quadrature error compensation signal to the mechanical resonator or the mechanical resonator measurement signal to reduce quadrature error in the mechanical resonator measurement signal error.