The optimal frequency estimation of a noisy sinusoidal signal

A signal-processing method is proposed whereby the frequency of a noisy sinusoidal signal can be estimated optimally. The criterion for optimum performance is the minimum observation time for a given error or the minimum error for a given observation time when the same signal-to-noise condition prevails. Three methods of analyzing the instance of the transition of the signal through a selected level in a given direction can be used to determine the frequency. These methods have been simulated, and the results give a comparison of the measurement errors for the various methods for different signal-to-noise ratios and observation times. The first two methods utilize only part of the available data for frequency measurements. The third method uses all available information (e.g., all the positive zero crossings) in order to arrive at a better estimation of the required information in a given observation time or to use less measuring time for a given error. These results illustrate the superior performance of the third method. The amount of calculations that have to be done to extract the required information is a disadvantage, but the computing power and speed of modern systems make this problem irrelevant when measuring the precision frequency of a proton magnetometer. This point must be taken into consideration, though, when higher-frequency signals have to be processed using this method