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Closed-form frequency estimator based on narrow-band approximation under noisy environment. (English) Zbl 1217.94070

Summary: 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.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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