Accurate Frequency Estimation of a Real Sinusoid by Three New Interpolators

Abstract

Interpolators are widely employed in the frequency estimation of sinusoidal signals. However, for a real-valued sinusoidal signal, the existing interpolators do not consider the negative frequency component, which leads to a frequency estimation error floor. To solve this problem and further improve the estimation accuracy, three new interpolators are proposed in this paper. These three new interpolators consist of two initial interpolators and one fine interpolator. In the proposed algorithm, the initial interpolators consider both the positive and negative frequency components and are utilized first to eliminate this error floor and obtain an initial frequency estimate. Then, the fine interpolator for the frequency estimation of a complex sinusoid is exploited to improve the accuracy of the initial frequency estimate. The theoretical analysis demonstrates that the frequency estimation mean square error of the proposed algorithm is almost equal to the Cramer–Rao lower bound. Compared with the existing time-domain analysis algorithms, the proposed algorithm has better estimation performance, especially in the case of a low signal-to-noise ratio. Compared with the existing frequency-domain analysis algorithms, the proposed algorithm has lower computational complexity and a wider valid estimation range.

Keywords

• Frequency estimation
• interpolation
• accuracy
• estimation error
• Cramer-Rao bounds
• root mean square