A Scalable Frequency Estimation Method Based on Multi-Point Interpolation of Trigonometric Functions

Abstract

Interpolation-based frequency estimation methods can be used to improve the frequency estimation accuracy of discrete Fourier transform (DFT) methods for complex exponential or real sinusoidal signals. However, traditional interpolation methods first need to search for the maximum spectral line and its adjacent spectral lines in order to interpolate the frequency estimate. This type of method has a low degree of flexibility and does not make full use of the effective information in the frequency domain. In order to solve this problem, this paper proposes a scalable frequency estimation method based on the multiple point interpolation of trigonometry, eliminating the need to find the peak of the spectrum and using multiple point spectral information to improve the frequency estimation accuracy. This paper first derives the formula for frequency estimation of complex sinusoidal signals using multiple spectral lines by using the trigonometric constant equation, then analyses the effects of frequency interval and number of selected frequency points on the frequency estimation error, and finally verifies the estimation performance of the proposed estimator against competing estimators by simulation. Simulation results show that the root mean square error (RMSE) of the estimator is closer to Cramér-Rao Lower Bound than those of the competing estimators over the whole effective signal-to-noise ratio range.