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

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.

Vibration Signal Extraction Based on FFT and Least Square Method

“…The influence of noise is also analyzed [27]- [28]. It is widely used due to easy implementation and high accuracy [29].…”

“…The methods mentioned above are accurate when processing a single component frequency signal (or two adjacent frequencies are far enough), but the accuracy is reduced significantly when spectral interference is serious. Luo [29] compares the accuracy of various interpolation methods with the Hanning window. When the normalized frequency approaches 1, negative frequency increases the spectral leakage and the frequency error.…”

An improved phase interpolation estimator

“…In the past several decades, a number of discrete spectrum correction methods were proposed, and each has its own merits and downsides [8]. The interpolation method is strongly associated with the category of the adopted window function, and interpolation formulas of different windows usually differ from each other [9][10][11]. As a result, it would be inconvenient for different windows to correct the frequency.…”

Frequency estimators with high resistance to interference from image frequency components

“…23 For this reason, several methods have been proposed in recent years that exhibit excellent resistance to image component interference. [23][24][25][26] One of the effective algorithms was proposed by Chen et al, 24 and Borkowski et al 25 further developed this approach, extending the range of application to maximum sidelobe decaying windows. In 2014, Belega et al 23 proposed an improved three-point interpolation algorithm that performs well in resisting image frequency component disturbances.…”