计及全泄漏影响的多点插值离散傅里叶变换校正方法

doi:10.19595/j.cnki.1000-6753.tces.190883

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摘要针对多频率短时波动周期情况, 提出基于全泄漏频谱抑制的多点插值离散傅里叶变换（DFT）校正方法。首先, 利用最大旁瓣衰减窗频谱线性比例递推特性, 将其他频率分量的频谱泄漏干扰以泰勒级数多项式等效近似, 结合被测频率的负频谱泄漏分量建立全泄漏频谱参数模型;然后, 根据谐波频谱泄漏的近似精度建立多谱线方程组, 通过精确求解得到最大旁瓣衰减窗下的多谱线频率插值校正通用解析表达式;最后, 采用最小二乘法得到幅值和相位的有效估计。多重仿真和实验测试结果表明, 在噪声和等量级的其他频率泄漏干扰下, 当被测频率低至1.5个频率分辨率时, 算法依然保持具有很高的校正精度。

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关键词 ：短时波动周期, 全泄漏, 多点插值离散傅里叶变换, 频谱参数模型

Abstract：A multipoint interpolated DFT correction method based on total spectral leakage suppression is proposed for the short cycles in record (CiR) of multi-frequency signal. Firstly, the spectral leakage from other frequency components is equivalently approximated to a Taylor series polynomial by the linear proportional recursive property of the maximum sidelobe decay Windows (MSDW) spectrum. The spectral parametric model of total spectral leakage is then established combined with the negative leakage component of the measured frequency. Furthermore, the corresponding equations of multipoint spectral lines are established according to the approximate order of the spectral leakage, and then the general analytical formula of multipoint frequency interpolation correction under the MSDW is derived. Finally, the least squares (LS) method is used to obtain an accurate estimation of the amplitude and phase. Multiple simulation and experimental test show that the algorithm still has high correction accuracy when the measured frequency is as low as 1.5 frequency resolutions under noise and other frequency leakage interference of equal magnitude.

Key words： Short cycles in record total spectral leakage multipoint interpolated discrete Fourier transform spectral parametric model

收稿日期: 2019-07-17

PACS:

TM935

通讯作者: 付志红男, 1966年生, 博士, 教授, 博士生导师, 主要研究方向为电能质量分析与电能计量、电力电子、电磁探测技术等。E-mail: fuzhihong@cqu.edu.cn

作者简介: 杨超男, 1986年生, 博士研究生, 研究方向为数字信号处理及其在电能计量和电能质量分析中的深度应用。E-mail: 328383369@qq.com

引用本文:

杨超, 张淮清, 王耀, 李波, 付志红. 计及全泄漏影响的多点插值离散傅里叶变换校正方法[J]. 电工技术学报, 2020, 35(16): 3385-3395. Yang Chao, Zhang Huaiqing, Wang Yao, Li Bo, Fu Zhihong. Multipoint Interpolated Discrete Fourier Transform Correction Method Considering Total Leakage Effect. Transactions of China Electrotechnical Society, 2020, 35(16): 3385-3395.

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