A method for detecting frequency mismatch in microelectromechanical systems (MEMS) gyroscopes is described. Detection of the frequency mismatch between a drive signal and a sense signal may be performed by generating an output signal whose spectrum reflects the physical characteristics of the gyroscope, and using the output signal to determine the frequency fC of the sense signal. The output signal may be generated by cross-correlating a random or pseudo-random noise signal with a response signal, where the response signal can be obtained by allowing the noise signal to pass through a system designed to have a noise transfer function that mimics the frequency response of the gyroscope. Since the noise signal is random or pseudo-random, cross-correlating the noise signal with the response signal reveals spectral characteristics of the gyroscope. To improve computational efficiency, the cross-correlation can be performed on demodulated versions of the noise signal and the response signal.