An optimal method for retrieving useful frequency information from a noisy sinusoidal signal

The author proposes a signal processing method whereby the frequency of a noisy sinusoidal signal can be estimated optimally. The criterion for optimum performance is the minimum measurement time for given error or the minimum error for a given measurement time when the same signal-to-noise condition prevails. Three methods of analyzing the instants of the transition of the signal through a selected level in a given direction can be used to determine the frequency. The first method measures the time between two consecutive positive zero crossings. The second method calculates the average period of the signal. With the third method every instant of transition through the same level is noted, thereby obtaining a sequence of equally spaced points, which can be approximated with least square error by a sequence of unequally spaced points, the interval of which can then be used to calculate an estimate of the frequency. These methods have been simulated, and the results give a comparison of the measurement errors for the various methods when different signal-to-noise ratios and measurement times are used