Accurate Frequency Estimator of Sinusoid Based on Interpolation of FFT and DTFT

Lei Fan,Jiyu Jin,Zhisen Wang,Jinyu Liu,Guoqing Qi,Jun Xing

doi:10.1109/access.2020.2977978

Lei Fan, Jiyu Jin + Show 4 more

Open Access

https://doi.org/10.1109/access.2020.2977978

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Abstract

An accurate frequency estimator of complex sinusoid in additive white noise is proposed. It is based on interpolation of Fast Fourier Transform (FFT) and Discrete-Time Fourier Transform (DTFT). Zero-padding is firstly performed before the FFT of the sinusoid sampled data, and the coarse estimate is obtained by searching the discrete frequency index of the maximum FFT spectrum line. Then the fine estimate is obtained by employing the maximum FFT spectrum line and two DTFT sample values located on the left and right side of the maximum spectrum line. The correlation coefficients between the Fourier Transform of the noises on two arbitrarily spaced spectrum lines are derived, and the MSE calculation formula is derived in additive white noise background based on the correlation coefficients. Simulations results demonstrate that the proposed algorithm has lower MSE than the competing algorithms, and its signal-to-noise ratio (SNR) threshold is lower compared with Candan algorithm, AM algorithm and Djukanovic algorithms.

Highlights

Sinusoidal frequency estimation can be applied in numerous fields such as radar, sonar, measurement, instrumentation, power systems, communications and so on
An accurate sinusoidal frequency estimation algorithm based on interpolation of Fast Fourier Transform (FFT) and Discrete-Time Fourier Transform (DTFT) is proposed in this paper
The fine estimate is obtained by employing the maximum FFT spectrum line and two DTFT sample values of the sinusoid located on the left and right side of the maximum FFT spectrum line

Summary

INTRODUCTION

Sinusoidal frequency estimation can be applied in numerous fields such as radar, sonar, measurement, instrumentation, power systems, communications and so on. Zero-padding is carried out before the FFT of the sinusoid sampled data, and the two neighboring spectrum line of the maximum FFT spectrum line are used for the fine estimation [8]. L. Fan et al.: Accurate Frequency Estimator of Sinusoid Based on Interpolation of FFT and DTFT windows are used, Candan method [6] and AM method [10] are generalized in [21]. The coarse estimate is obtained by finding the discrete frequency index of the maximum FFT spectrum line. The fine estimate is obtained by employing the maximum FFT spectrum line and two DTFT sample values of the sinusoid located on the left and right side of the maximum FFT spectrum line.

PROPOSED ALGORITHM

THEORETICAL ANALYSIS The 2N-point DFT of is as follows

EXPERIMENTAL RESULTS

CONCLUSION