Statistical frequency measuring error of the quadrature demodulation technique for noisy single-tone pulse signals

The standard deviation of the centre frequency of a signal is investigated for the quadrature demodulation technique (QDT). Signal frequencies can be measured by QDT unaffected by the amount of available signal periods. It can be used for the measurement of nonstationary signals generated by laser Doppler velocimeters. The dependence of the frequency measuring error on the averaging time of noisy single-tone Gaussian pulse signals is analysed. Assuming a quantum noise process, it is shown that the minimum measuring error results for an averaging time of approximately 1/ e 2 of the pulse duration of the signal. Alternatively, defined weighting of the measured values leads to a monotonically decreasing measuring error with increasing averaging time until the Cramer–Rao lower bound is reached. Therefore, the weighted QDT provides the lowest measuring error of all linear unbiased frequency estimators. It allows the evaluation of small frequency changes of laser Doppler signals, e.g. from micro-turbulent flows. The theory presented here is verified by Monte Carlo simulations and experiments.