基于频域伸缩的改进DFT算法

Improved DFT algorithm based on frequency domain expansion

离散傅里叶变换是对电力系统稳态信号进行频谱分析的最基本数学工具,也是国际电工委员会推荐用于谐波和间谐波测量的变换方法。该方法在分析窗口长度与实际信号周期不符时,各单独的谐波成分在频域会出现栅栏效应。文章提出一种基于频域伸缩的改进DFT算法,该方法将频域信号做了适当伸缩,能直接在离散谱线上得到幅值和相角,克服了栅栏效应,避免了插值运算,从而提高了效率。利用MATLAB分别仿真加窗和噪声对算法的影响,并和其他方法进行比较。仿真结果证明了基于频域伸缩的改进DFT算法的有效性,准确性和稳定性。

Discrete Fourier transformer is the most basic mathematical tool for the spectrum analysis of a stable electrical signal,and also the transformation approach recommended by International Electrotechnical Commission for harmonics and inter- harmonics measurement. But for this method,when the analyzed window length does not match the actual signal cycle,the fence effect will appear for the individual harmonic components in the frequency domain. An improved DFT algorithm based on frequency domain expansion was proposed in this paper. This algorithm made the frequency domain signal expanded and contracted appropriately so that the amplitude and phase angle could be obtained directly on the discrete spectral lines. Thus,the fence effect was overcome,the interpolation operation was avoided,and thereby the efficiency was improved. Then simulation was made by using MATLAB to test the impact of noise and windowing on the algorithm,and finally the new algorithm was compared with other methods. Simulation results verified the effectiveness,accuracy and stability of the improved DFT algorithm based on frequency domain expansion.