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

Authors:
Gang Wei;Cui Yang;Fang-jiong Chen
Affiliations:
School of Electronic and Information Engineering, South China University of Technology, 381 Wushan Road, Guangzhou 510640, Guangdong Province, China;School of Electronic and Information Engineering, South China University of Technology, 381 Wushan Road, Guangzhou 510640, Guangdong Province, China;School of Electronic and Information Engineering, South China University of Technology, 381 Wushan Road, Guangzhou 510640, Guangdong Province, China
Venue:
Signal Processing
Year:
2011

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Abstract

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.