Abstract：The sliding discrete Fourier transform (DFT) can experience instability issues due to the accumulation and amplification of the errors introduced by the finite-word-length effects in real practical discrete systems. In this paper, the quantization noise of A-D, the quantization error of the twiddle factors, and the rounding error of arithmetic operations are taken into consideration to analyze their influences on the stability of the sliding DFT based on the statistical properites of random signals. Based on the detailed analysis, it is revealed that the rounding error of arithmetic operations is the key reason to cause the unstable phenomenon. Both simulation and experimental results validate the theoretical analysis of instability issue of the sliding DFT. To deal with this instability problem, two methods are proposed to eliminate the error accumulation and amplification through swapping the calculation sequences of the sliding DFT. Extensive simulations and experiments are provided to verify the effectiveness of the proposed solutions.
刘华吾,胡海兵,邢岩. 有限字长对滑动窗DFT稳定性的影响研究[J]. 电工技术学报, 2016, 31(11): 22-31.
Liu Huawu Hu Haibing Xing Yan. Research of Finite-Word-Length Effects on the Stability of the Sliding DFT. Transactions of China Electrotechnical Society, 2016, 31(11): 22-31.
[1] 王尧,李奎,任伯飞,等.基于全相位傅里叶变换的磁调制交直流漏电电流检测方法[J].电工技术学报,2015,30(18):254-260. Wang Yao,Li Kui,Ren Bofei,et al.Study of fluxgate current detecting method for AC-DC earth leakage current based on apFFT[J].Transactions of China Electrotechnical Society,2015,30(18):254-260. [2] 孙晓云,同向前,高鑫.柔性直流输电系统中IGBT阀的故障诊断方法[J].电工技术学报,2014,29(8):235-241. Sun Xiaoyun,Tong Xiangqian,Gao Xin,et al.Research on the fault diagnosis of IGBT valve in VSC-HVDC[J].Transactions of China Electrotechnical Society,2014,29(8):235-241. [3] 曾博,唐求,卿柏元,等.基于Nuttall自卷积窗的改进FFT谱分析方法[J].电工技术学报,2014,29(7):59-65. Zeng Bo,Tang Qiu,Qing Baiyuan,et al.Spectral analysis method based on improved FFT by Nuttall selfconvolution window[J].Transactions of China Electrotechnical Society,2014,29(9):59-65. [4] 王兴贵,刘正英.基于载波变幅移相调制方法的串联型微网功率平衡控制[J].电力系统保护与控制,2015,43(13):38-44. Wang Xinggui,Liu Zhengying.Series micro-grid power balance control based on carrier amplitude variation and[J].Power System Protection and Control,2015,43(13):38-44. [5] 徐建,张语勍,李彦斌,等.短时傅里叶变换和S变换用于检测电压暂降的对比研究[J].电力系统保护与控制,2014,12(16):44-48. Xu Jian,Zhang Yuqing,Li Yanbin,et al.Comparative study of STFT and S transform on detecting voltage sag[J].Power System Protection and Control,2014,12(16):44-48. [6] 郁祎琳,徐永海,刘晓博.滑窗迭代DFT的谐波电流检测方法[J].电力系统保护与控制,2011,39(13):78-90. Yu Yilin,Xu Yonghai,Liu Xiaobo.Study of harmonic current detection based on sliding-window iterative algorithm of DFT[J].Power System Protection and Control,2011,39(13):78-90. [7] Jacobsen E,Lyons R.The sliding DFT[J].IEEE Signal Processing Magazine,2003,20(3):74-80. [8] Jacobsen E,Lyons R.An update to the sliding DFT[J].IEEE Signal Processing Magazine,2004,21(1):110-111. [9] 王宏伟.基于傅里叶变换的数字信道化及相关技术[D].西安:西安电子科技大学,2010. [10]Carlos M O,Ignacio C,Sebastian M,et al.Harmonics measurement with a modulated sliding discrete Fourier transform algorithm[J].IEEE Transactions on Instrumen-tation and Measurement,2014,63(4):781-793. [11]周柯,罗安,汤赐,等.一种大功率混合注入式有源电力滤波器的工程应用[J].中国电机工程学报,2007,27(22):80-86. Zhou Ke,Luo An,Tang Ci,et al.High-power hybrid injection active power filter’s engineering application[J].Proceedings of the CSEE,2007,27(22):80-86. [12]Ni Ruoshui,Li Yunwei,Zhang Ye,et al.Virtual impedance based selective harmonic compensation(VI-SHC)PWM for current source rectifiers[J].IEEE Transactions on Power Electronics,2014,29(7):3346-3356. [13]Reza M S,Ciobotaru M,Agelidis V G.Accurate estimation of single-phase grid voltage parameters under distorted conditions[J].IEEE Transactions on Power Delivery,2014,29(3):138-1146. [14]Kim J H,Chang T G.Analytic derivation of the finite word-length effect of the twiddle factors in recursive implementation of the sliding DFT[J].IEEE Transactions on Signal Processing,2000,48(5):1485-1488. [15]王宏伟.滑动离散傅立叶算法输出稳定性研究[J].电波科学学报,2012,27(4):773-779. Wang Hongwei.Output stabilization of sliding discrete Fourier transform algorithm[J].Chinese Journal of Radio Science,2012,27(4):773-779. [16]Darwish H A,Fikri M.Practical considerations for recursive DFT implementation in numerical relays[J].IEEE Transactions on Power Delivery,2007,22(1):42-49. [17]Duda K.Accurate,guaranteed stable,sliding discrete fourier transform[J].IEEE Signal Processing Magazine,2010,27(6):124-127. [18]Neves F A S,Souza H E P,Cavalcanti M C,et al.Digital filters for fast harmonic sequence component separation of unbalanced and distorted three-phase signals[J].IEEE Transactions on Industrial Electronics,2012,59(10):3847-3859. [19]Neves S,Arcanjo C,Azevedo S,et al.The SVFT-Based Control[J].IEEE Transactions on Industrial Electronics,2014,61(8):4152-4160. [20]Borisov K,Ginn H,Chen G.A computationally efficient RDFT-based reference signal generator for active compensators[J].IEEE Transactions on Power Delivery,2009,24(4):2396-2404. [21]Ginn H L,Chen Guangda.Digital control method for grid-connected converters supplied with nonideal voltage[J].IEEE Transactions on Industrial Informatics,2014,10(1):127-136. [22]Chen Guangda,Jiang Yingying,Zhou Haiguo.Practical issues of recursive DFT in active power filter based on CPC power theory[C]//Proceedings of Power and Energy Engineering Conference,Wuhan,2009:1-5. [23]McGrath B P,Holmes D G,Galloway J J H.Power converter line synchronization using a discrete Fourier transform(DFT)based on a variable sample rate[J].IEEE Transactions on Power Electronics,2005,20(4):877-884. [24]Yang Junzhe,Liu Chihwen.A precise calculation of power system frequency[J].IEEE Transactions on Power Delivery,2001,16(3):361-366. [25]胡广书.数字信号处理——理论、算法与实现[M].3版.北京:清华大学出版社,2012:406-425. [26]常建平,李海林.随机信号分析[M].北京:科学出版社,2006:82-94.
2016, Vol. 31 
