Closed-form frequency estimator based on narrow-band approximation under noisy environment

A new method for single sinusoidal frequency estimation in closed-form formula is proposed. Since sinusoidal signals are narrow-banded and white noise distribution is statistically equal in the whole spectrum, a narrow-band signal extracted from the Fourier transform of the original signal can be used to approximate the noise-corrupted sinusoidal signal. A concise closed-form formula is then deduced to estimate the frequency based on the narrow-band signal. Performance analysis and simulation results are presented, showing that the new algorithm has close performance to the Cramer–Rao bound, especially under low SNRs. It is also demonstrated that the method can be easily generalized to multi-sinusoidal signals.