Generalization of interpolation DFT algorithms and frequency estimators with high image component interference rejection

Jiufei Luo,Xinyi Li,Shuaicheng Hou,Yi Zhang,Qi Ouyang

doi:10.1186/s13634-016-0330-6

Abstract

This paper focuses on the problem of frequency estimation of noise-contaminated sinusoidal. A basic tool to solve this problem is the interpolated discrete Fourier transform (DFT) algorithms, in which the influences of the spectral leakage from negative frequency are often neglected, resulting in significant errors in estimation when the signals contained small cycles. In this paper, analytic expressions of the interference due to the image component are derived and its influences on the traditional two-point interpolated DFT algorithms are analyzed. Based on the achieved expressions, the interpolated DFT algorithms are generalized and a novel frequency estimator with high image component interference rejection is proposed. Simulation results show that the frequency errors returned by the new algorithm are very small even though only one or two cycles are obtained. Comparative studies indicate that the new algorithm also has a good performance in the noise condition. With the advantages of high precision and strong robustness against additive noise, the proposed algorithm is a good choice for frequency estimation when the negative frequency interference is the dominant error source.

Highlights

1 Introduction Spectral analysis based on the discrete Fourier transform (DFT) and implemented by the fast Fourier transform (FFT) has been widely used in many fields for several decades
We proposed a novel frequency estimator by which the leakage coming from image component can be further reduced compared with the algorithm proposed by Belega et al More importantly, it keeps good noise properties due to a two-point-based mechanism
6 Conclusions Frequency estimation by the interpolation discrete Fourier transform (IpDFT) method is studied in this paper

Summary

Introduction

Spectral analysis based on the discrete Fourier transform (DFT) and implemented by the fast Fourier transform (FFT) has been widely used in many fields for several decades. The algorithms may become quite vulnerable if cos(φ0 + δπ) ≈ 0 or sin(φ0 + δπ) ≈ 0 Under such two circumstances, the imaginary parts or the real parts would be so small that even a small disturbance would lead to a dramatic change in αR or αI, resulting of significant errors in the final frequency estimates. The fact that αR and αI (including various kinds of mean values of the two) are phase independent and the change of phase has no influences on frequency estimates help us get a robust ratio by time-shifting technique. We can obtain the spectral lines l and l ± 1 of the time-delayed sequence by means of the sliding discrete Fourier transform (SDFT) [19, 20] It will be more efficient compared with another separate FFT or DFT. As λ0 is unknown, we can use its largest bin number l, instead

Theoretical cosine wave without noise

Conclusions