Adaptive algorithm for direct estimation of sinusoidal frequency

An adaptive direct frequency estimation (DFE) algorithm is proposed for tracking the frequency of a real sinusoid embedded in white noise with known variance. Using a least mean square-style algorithm, the frequency estimate is adjusted directly on a sample-by-sample basis. The learning behavior and mean square error of the estimated delay are derived and verified by computer simulations. DFE show the most accurate estimation performance when the frequency is equal to 0.5 π while its learning is slow and frequency variance is large if the frequency is close to 0 or π.