基于局部余弦变换和小波变换的短时电能质量扰动检测
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摘要
随着国民经济的迅速发展和电力市场的逐步形成,电能质量问题已经成为众多领域关注的热点。必须建立电能质量检测和分析系统,实现对各种电能质量问题的故障定位和特征提取。这是治理和改善电能质量的必要前提和依据。
本文首先阐述了电能质量的相关概念,介绍了各种电能质量现象及相关标准。其中,对几种有代表性的短时电能质量扰动作了详尽而细致的描述,分析了它们的扰动特征,分别是:电压凹陷、电压凸起和电压中断;短时间谐波和时变谐波;高频暂态扰动,包括暂态振荡和暂态脉冲等。
目前的电能质量检测和分析方法大致可分为时域仿真法、频域模拟法和基于变换的方法。小波变换作为第三类方法中的典型,近年来已成为各专家和学者的研究热点。但电能质量问题种类众多,且扰动特性各有不同,现有方法虽然各有其特点,但还不足以很好解决对各种电能质量扰动特别是短时电能质量扰动的检测,尚需进一步研究和完善现有的检测与分析方法。本文提出了将局部余弦变换引进到电能质量检测领域,结合现有检测和分析方法,重点研究和探讨了局部余弦变换和小波变换的分析方法。
结合小波检测中的两个难点一时变谐波检测和信号噪声问题,具体研究了如何将局部余弦变换应用到电能质量扰动信号的检测和分析。
首先探讨了如何利用局部余弦变换和差变算法实现噪声环境下的短时电压变化的检测。
然后研究了如何利用局部余弦变换对信号时频的划分实现对短时谐波的检测分析以及如何通过局部最佳余弦基的搜索分析时变谐波。
With the rapid growth of national economy and formation of power market, power quality has become the focus of many fields. It is necessary to set up power quality monitor and analysis system, which can realize fault location and character extraction to all power quality disturbances. It is the premise and reference of improve and harness power quality.Firstly this paper expands relative concept about power quality, introduces all power quality issues and their standard. Among those several representative short-term power quality disturbances are introduced particularly, and their characteristics are analyzed. They are: voltage sag, voltage swell and voltage interruption; transient harmonic and time-varying harmonic; transient disturbances, including transient oscillation and transient pulses.Generally power quality detection methods can be generalized in three types: time domain simulation, frequency domain simulation and methods based on transform. Wavelet transform has become study focus of many experts and scholars as representative of the third type. However, power quality issues have many types, and they have different characters. Sometimes wavelet transform can't treat all power quality issues especially short-term power quality disturbances. It is necessary that add other method to make up the shortage of wavelet transform. This paper introduces local cosine transform (LCT) to power quality detection. This paper expounds fundamental principle and time-frequency character of wavelet transform
and local cosine transform.We discuss how to apply local cosine transform to power quality disturbance detecting considering two difficulty in wavelet analysis - time-varying harmonic detection and signal noises.Firstly we discuss how to detecting fundamental frequency disturbances in noises through noises robustness of LCT coefficients and difference algorithm.How to use local cosine transform to detect short time harmonics, how to search LCT optimum base to analyze time-varying harmonic are emphasis of this paper.Finally we explain how to utilize wavelet transform module maximum filtering signal noises and analyzing high frequency transient disturbances.After simulation and comparing with other methods we know this method has preferable performance. Analyzing power quality issues using this method can get satisfactory results. This method makes up the singleness and shortage of wavelet analysis in power quality detection. It provides a new approach in this field.In the end we point out some place need improving of this method.
本文首先阐述了电能质量的相关概念,介绍了各种电能质量现象及相关标准。其中,对几种有代表性的短时电能质量扰动作了详尽而细致的描述,分析了它们的扰动特征,分别是:电压凹陷、电压凸起和电压中断;短时间谐波和时变谐波;高频暂态扰动,包括暂态振荡和暂态脉冲等。
目前的电能质量检测和分析方法大致可分为时域仿真法、频域模拟法和基于变换的方法。小波变换作为第三类方法中的典型,近年来已成为各专家和学者的研究热点。但电能质量问题种类众多,且扰动特性各有不同,现有方法虽然各有其特点,但还不足以很好解决对各种电能质量扰动特别是短时电能质量扰动的检测,尚需进一步研究和完善现有的检测与分析方法。本文提出了将局部余弦变换引进到电能质量检测领域,结合现有检测和分析方法,重点研究和探讨了局部余弦变换和小波变换的分析方法。
结合小波检测中的两个难点一时变谐波检测和信号噪声问题,具体研究了如何将局部余弦变换应用到电能质量扰动信号的检测和分析。
首先探讨了如何利用局部余弦变换和差变算法实现噪声环境下的短时电压变化的检测。
然后研究了如何利用局部余弦变换对信号时频的划分实现对短时谐波的检测分析以及如何通过局部最佳余弦基的搜索分析时变谐波。
With the rapid growth of national economy and formation of power market, power quality has become the focus of many fields. It is necessary to set up power quality monitor and analysis system, which can realize fault location and character extraction to all power quality disturbances. It is the premise and reference of improve and harness power quality.Firstly this paper expands relative concept about power quality, introduces all power quality issues and their standard. Among those several representative short-term power quality disturbances are introduced particularly, and their characteristics are analyzed. They are: voltage sag, voltage swell and voltage interruption; transient harmonic and time-varying harmonic; transient disturbances, including transient oscillation and transient pulses.Generally power quality detection methods can be generalized in three types: time domain simulation, frequency domain simulation and methods based on transform. Wavelet transform has become study focus of many experts and scholars as representative of the third type. However, power quality issues have many types, and they have different characters. Sometimes wavelet transform can't treat all power quality issues especially short-term power quality disturbances. It is necessary that add other method to make up the shortage of wavelet transform. This paper introduces local cosine transform (LCT) to power quality detection. This paper expounds fundamental principle and time-frequency character of wavelet transform
and local cosine transform.We discuss how to apply local cosine transform to power quality disturbance detecting considering two difficulty in wavelet analysis - time-varying harmonic detection and signal noises.Firstly we discuss how to detecting fundamental frequency disturbances in noises through noises robustness of LCT coefficients and difference algorithm.How to use local cosine transform to detect short time harmonics, how to search LCT optimum base to analyze time-varying harmonic are emphasis of this paper.Finally we explain how to utilize wavelet transform module maximum filtering signal noises and analyzing high frequency transient disturbances.After simulation and comparing with other methods we know this method has preferable performance. Analyzing power quality issues using this method can get satisfactory results. This method makes up the singleness and shortage of wavelet analysis in power quality detection. It provides a new approach in this field.In the end we point out some place need improving of this method.
引文
[1] 吴竞昌.供电系统谐波.北京:中国电力出版社,1998
[2] 林雪海.论电能质量标准.中国电力,1997,30(3):8-10
[3] Y. Liao, J B Lee. A fuzzy-expert system for classifying power quality disturbances. Electrical Power and Energy Systems 26(2004): 199-205
[4] S J Huang et al. Application of wavelets to classify power system disturbances. Electric Power Systems Research 47(1998): 87-93
[5] A. M. Gaouda et al. On-line disturbance classification using nearest neighbor rule. Electric Power Systems Research 57(2001): 1-8
[6] A M Gaouda, S H Kanoun, M. M. A. Salama, A. Y. Chikhani. Pattern Recognition Applications for Power System Disturbance Classification. IEEE Transaction on Power Delivery, 2002, 17(3): 677-683
[7] G ZHENG, M X Shi et al. Power quality disturbance classification based on rule-based and wavelet multi-resolution decomposition. Proceeding of the First International Conference on Machine Learning and Cybernetics, Beijing, 4-5 November 2002
[8] A M Gaouda, S H Kanoun, M. M. A. Salama, A. Y. Chikhani. Wavelet-based signal processing for disturbance classification and measurement. IEE Proc.-Gener. Transm. Distrib, 2002, 19(3): 310-318
[9] 胡铭,陈珩.基于小波变换模极大值的电能质量扰动检测与定位,电网技术,2001,25(3):12-16
[10] 周文晖,李青,周兆经.采用小波多分辨率信号分解的电能质量检测,电工技术学报,2001,16(6):81-84
[11] 陈祥训.采用小波技术的几种电能质量扰动的测量与分类方法.中国电机工程学报,2002,22(10):1-6
[12] 任震,黄群古,黄雯莹,张勇军.4种新的小波变换及其在发电机故障信号分析中的应用,电力系统自动化,2001,25(1):50-54
[13] 张秀娟,徐永海,肖湘宁.电能质量扰动小波变换检测与识别方法的发展,电力自动化设备.2003,23(9):67-71
[14] Santoso S, Grady W M, Powers E J. Characterization of distribution power quality events with Fourier and wavelet transforms. IEEE Transactions on Power Delivery, 2000, 15(1): 247-254
[15] Yan J B, Liu X C, Yang H Geng. Analysis of short-term power system disturbance based-on modulo maximum principle and energy distribution curve of wavelet transform. Power System Technology, 2002, 26(4): 16-18, 33
[16] Ribeiro P F. Wavelet transform: An advanced tool for analyzing non-stationary harmonic distortions in power systems. Proceedings of IEEE ICHPS Ⅵ, Bologna, Italy, September 21-23, 1994, 365-369.
[17] 郑健超,陈祥训,覃剑.验证小波变换行波故障测距法的现场试验.电网技术,2001,25(3):26-29.
[18] Huang S J, Hsieh C T. Coiflet wavelet transform applied to inspect power system disturbance-generated signals. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(1): 204-210
[19] Johan Driesen, Craenenbroeck T V, Reekmans R et al. Analyzing time-varying power system harmonics using wavelet transform. IEEE Instru-mentation and Measurement Technology Conference, Srussels, Beigium, 1996: 474-479
[20] 吴军基,刘皓明,孟绍良.小波滤波器在电力系统谐波检测中的应用.电力系统及其自动化学报,1999,11(5-6):50-53.
[21] 杨桦,唐卓尧,任震.基于小波变换检测谐波的新方法.电力系统自动化,1997,21(10):39-42.
[22] 张昊,石铁洪,刘沛.基于双正交小波和复小波的次同步谐振检测方法.中国电机工程学报.2001,21(3):12-15,52
[23] 张昊,石铁洪,刘沛.基于B样条小波预处理的短窗算法.中国电机工程学报,2000,20(10):50-54.
[24] 任震,黄群古,黄雯莹,等.基于多频带小波变换的电力系统谐波分析新方法.中国电机工程学报,2000,20(12):38-41,46.
[25] 王建赜,冉启文,纪延超,等.基于小波变换的时变谐波检测.电力系统自动化,1998,22(8):52-55.
[26] Surga Santoso, Edward J Powers, Grady W Mack. Electric power quality disturbance detection using wavelet transform analysis. The IEEE SP International Symposium on Time-frequency and Time-Scale analysis, Philadelphia, PA, U. S. A, 1994, 166-169.
[27] Brito N S D, Souza B A, Pires F A C. Daubechies wavelets in quality of electrical power. The 1998 ICHQP, Athens, Greece, 511-515.
[28] Wilkinson W A, Cox M D. Discrete wavelet analysis of Power system transients. IEEE Transactions on power systems, 1996, 11(4): 2038-2044.
[29] Olivier Poisson, Pascal Rioual, Michel Meunier. Detection and measurement of power quality disturbances using wavelet transform. IEEE Transaction on power delivery, 2000, 15(3): 1039-1044.
[30] Angrisani L, Daponte P, Apuzzo M D. A measurement method based on the wavelet transform for power quality analysis. IEEE Transaction on Power delivery, 1998, 13(4): 990-998.
[31] 王建赜,纪延超,冉启文,等.小波变换在电能质量分析中的应用.继电器,1999,27(5):13-19.
[32] 陈祥训.正交紧支复小波的生成及其在电力系统的应用.中国电机工程学报,2000,20(7):83-88.
[33] 何建军,任震,黄雯莹,等.电力系统奇异信号的复值小波分析.中国电机工程学报,1999,19(11):1-4,51.
[34] 董新洲,耿中行,葛耀中,等.小波变换应用于电力系统故障信号分析初探.中国电机工程学报,1997,17(6):421-424.
[35] 石志强,任震,黄雯莹.基于B-小波的异步电机故障信号去噪和检测.电力系统自动化,1997,21(6):38-41.
[36] 王钰,徐大可,李彦明,等.小波变换在变压器绕组变形诊断中的应用.高电压技术,1997,23(4):15-18.
[37] 王哲,蔡惟铮,陈学允,等.基于小波分析的高压变压器局部放电在线监测.电力系统自动化.1998.22(4):19-23.
[38] 全玉生,李洪杰,严璋.应用小波变换测量间断角的新方法.电力系统自动化.1998,22(1):33-35.
[39] 王渝红,黄雯莹,任震,等.离散二进小波变换及其在电机故障分析中的应用.电力 系统自动化,1995,19(12):20-24.
[40] 王国利,郝艳捧,何义,等.小波变换去噪在高压冲击波形参数提取中的应用.高电压技术,2000,(5):9-12.
[41] 何正友,戴小文,钱清泉.电力系统暂态信号的小波分析方法及其应用(二)电力系统暂态信号的小波分析方法探讨.电力系统及其自动化学报,2002,14(5):1-3,24,33
[42] 岳蔚,刘沛.基于数学形态学消噪的电能质量扰动检测法.电力系统自动化,2002,26(7):13-17
[43] 王庆禹,褚福磊.小波变换中的能量泄漏问题.机械科学与技术,2001,20(1):12-13,16
[44] 张宇辉,陈晓东,王鸿懿.基于连续小波变换的电能质量测量与分类.电力自动化设备,2004,24(3):17-21
[45] 李天云,陈晓东,赵为红等.几种短时电能质量扰动分类和检测的双小波分析法.电力系统自动化,2003,27(22):26-29
[46] 刘安定,肖先勇,邓武军.短时电能质量扰动检测的一种新方法.继电器,2005,33(8):27-33
[47] 刘安定,肖先勇,邓武军.基于DCT/WT的电能质量扰动检测分析.电网技术,2005,29(10)
[48] Nara K, Hasegawa Oyama T, et, al. Forwarding to Future Power Delivery System. In: Proceeding of IEEE ICHQP Ⅸ. Orlando(USA): 2000, 8-18
[49] Dugan R C, McGranaghan M F, Beaty H W. Electrical Power System Quality. New York: McGraw-Hill, 1996
[50] 王成山,王继东.基于小波包分解的电能质量扰动分类方法.电网技术,2004,28(15):78-82
[51] 岳蔚,刘沛.基于数学形态学消噪的电能质量扰动检测方法.电力系统自动化,2002,26(7):13-17
[52] Hussain A, Sukairi M H, Mohamed A. Automatic detection of power quality disturbances and identification of transient signals. Proceedings of the Sixth International Symposium on Signal Processing and its Applications, 2001, 2(2): 462-465
[53] Poisson O, Rioual P, Meunier M. Detection and measurement of power quality disturbances using wavelet transform. IEEE transactions on Power Delivery, 2000, 15(3): 1039-1044
[54] 杨福生.小波变换的工程分析与应用.北京,科学出版社,1999
[55] Stephane Mallat. A Wavelet Tour of Signal Processing. BeiJing, China Machine Press, 2002
[56] Auscher P, Weiss G, Wickerhauser M V. Local Sine and Cosine Base of Coifman and Meyer and the Construction of Smooth Wavelet. Wavelets: A Tutorial in Theory and Application, Academic Press, 1992: 237-256
[57] Chen C T, Oonoho O. Atomic decomposition by basis pursuit. SPIE international Conference on Wavelet, San Diego, 1995
[58] Qiang C, Huang T S. Robust optimum detection of transform domain multiplicative watermarks. IEEE Transactions on Signal Processing, 2003, 51(4): 906-924
[59] Dong E, Zhao n M, Li Yongli. Low bit and variable rate speech coding using local cosine transform. 2002 IEEE Region 10 Annual International Conference on Computer, Communications, Control and Power Engineering, Proceedings, 2002, 1(1): 423-426
[60] Hamid E Y, Kawasaki Z L, Madiana R. Method for RMS and power measurements based on the wavelet packet transform. IEE Proceedings: Science, Measurement and Technology, 2002, 149(2): 60-66
[61] Meliopoulas A P S, Fardanesh B, Zelingher S. Harmonic measurement system via synchronized measurements. 2000 Power Engineering Society Summer Meeting, 2000, 2(2): 1094-1100
[2] 林雪海.论电能质量标准.中国电力,1997,30(3):8-10
[3] Y. Liao, J B Lee. A fuzzy-expert system for classifying power quality disturbances. Electrical Power and Energy Systems 26(2004): 199-205
[4] S J Huang et al. Application of wavelets to classify power system disturbances. Electric Power Systems Research 47(1998): 87-93
[5] A. M. Gaouda et al. On-line disturbance classification using nearest neighbor rule. Electric Power Systems Research 57(2001): 1-8
[6] A M Gaouda, S H Kanoun, M. M. A. Salama, A. Y. Chikhani. Pattern Recognition Applications for Power System Disturbance Classification. IEEE Transaction on Power Delivery, 2002, 17(3): 677-683
[7] G ZHENG, M X Shi et al. Power quality disturbance classification based on rule-based and wavelet multi-resolution decomposition. Proceeding of the First International Conference on Machine Learning and Cybernetics, Beijing, 4-5 November 2002
[8] A M Gaouda, S H Kanoun, M. M. A. Salama, A. Y. Chikhani. Wavelet-based signal processing for disturbance classification and measurement. IEE Proc.-Gener. Transm. Distrib, 2002, 19(3): 310-318
[9] 胡铭,陈珩.基于小波变换模极大值的电能质量扰动检测与定位,电网技术,2001,25(3):12-16
[10] 周文晖,李青,周兆经.采用小波多分辨率信号分解的电能质量检测,电工技术学报,2001,16(6):81-84
[11] 陈祥训.采用小波技术的几种电能质量扰动的测量与分类方法.中国电机工程学报,2002,22(10):1-6
[12] 任震,黄群古,黄雯莹,张勇军.4种新的小波变换及其在发电机故障信号分析中的应用,电力系统自动化,2001,25(1):50-54
[13] 张秀娟,徐永海,肖湘宁.电能质量扰动小波变换检测与识别方法的发展,电力自动化设备.2003,23(9):67-71
[14] Santoso S, Grady W M, Powers E J. Characterization of distribution power quality events with Fourier and wavelet transforms. IEEE Transactions on Power Delivery, 2000, 15(1): 247-254
[15] Yan J B, Liu X C, Yang H Geng. Analysis of short-term power system disturbance based-on modulo maximum principle and energy distribution curve of wavelet transform. Power System Technology, 2002, 26(4): 16-18, 33
[16] Ribeiro P F. Wavelet transform: An advanced tool for analyzing non-stationary harmonic distortions in power systems. Proceedings of IEEE ICHPS Ⅵ, Bologna, Italy, September 21-23, 1994, 365-369.
[17] 郑健超,陈祥训,覃剑.验证小波变换行波故障测距法的现场试验.电网技术,2001,25(3):26-29.
[18] Huang S J, Hsieh C T. Coiflet wavelet transform applied to inspect power system disturbance-generated signals. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(1): 204-210
[19] Johan Driesen, Craenenbroeck T V, Reekmans R et al. Analyzing time-varying power system harmonics using wavelet transform. IEEE Instru-mentation and Measurement Technology Conference, Srussels, Beigium, 1996: 474-479
[20] 吴军基,刘皓明,孟绍良.小波滤波器在电力系统谐波检测中的应用.电力系统及其自动化学报,1999,11(5-6):50-53.
[21] 杨桦,唐卓尧,任震.基于小波变换检测谐波的新方法.电力系统自动化,1997,21(10):39-42.
[22] 张昊,石铁洪,刘沛.基于双正交小波和复小波的次同步谐振检测方法.中国电机工程学报.2001,21(3):12-15,52
[23] 张昊,石铁洪,刘沛.基于B样条小波预处理的短窗算法.中国电机工程学报,2000,20(10):50-54.
[24] 任震,黄群古,黄雯莹,等.基于多频带小波变换的电力系统谐波分析新方法.中国电机工程学报,2000,20(12):38-41,46.
[25] 王建赜,冉启文,纪延超,等.基于小波变换的时变谐波检测.电力系统自动化,1998,22(8):52-55.
[26] Surga Santoso, Edward J Powers, Grady W Mack. Electric power quality disturbance detection using wavelet transform analysis. The IEEE SP International Symposium on Time-frequency and Time-Scale analysis, Philadelphia, PA, U. S. A, 1994, 166-169.
[27] Brito N S D, Souza B A, Pires F A C. Daubechies wavelets in quality of electrical power. The 1998 ICHQP, Athens, Greece, 511-515.
[28] Wilkinson W A, Cox M D. Discrete wavelet analysis of Power system transients. IEEE Transactions on power systems, 1996, 11(4): 2038-2044.
[29] Olivier Poisson, Pascal Rioual, Michel Meunier. Detection and measurement of power quality disturbances using wavelet transform. IEEE Transaction on power delivery, 2000, 15(3): 1039-1044.
[30] Angrisani L, Daponte P, Apuzzo M D. A measurement method based on the wavelet transform for power quality analysis. IEEE Transaction on Power delivery, 1998, 13(4): 990-998.
[31] 王建赜,纪延超,冉启文,等.小波变换在电能质量分析中的应用.继电器,1999,27(5):13-19.
[32] 陈祥训.正交紧支复小波的生成及其在电力系统的应用.中国电机工程学报,2000,20(7):83-88.
[33] 何建军,任震,黄雯莹,等.电力系统奇异信号的复值小波分析.中国电机工程学报,1999,19(11):1-4,51.
[34] 董新洲,耿中行,葛耀中,等.小波变换应用于电力系统故障信号分析初探.中国电机工程学报,1997,17(6):421-424.
[35] 石志强,任震,黄雯莹.基于B-小波的异步电机故障信号去噪和检测.电力系统自动化,1997,21(6):38-41.
[36] 王钰,徐大可,李彦明,等.小波变换在变压器绕组变形诊断中的应用.高电压技术,1997,23(4):15-18.
[37] 王哲,蔡惟铮,陈学允,等.基于小波分析的高压变压器局部放电在线监测.电力系统自动化.1998.22(4):19-23.
[38] 全玉生,李洪杰,严璋.应用小波变换测量间断角的新方法.电力系统自动化.1998,22(1):33-35.
[39] 王渝红,黄雯莹,任震,等.离散二进小波变换及其在电机故障分析中的应用.电力 系统自动化,1995,19(12):20-24.
[40] 王国利,郝艳捧,何义,等.小波变换去噪在高压冲击波形参数提取中的应用.高电压技术,2000,(5):9-12.
[41] 何正友,戴小文,钱清泉.电力系统暂态信号的小波分析方法及其应用(二)电力系统暂态信号的小波分析方法探讨.电力系统及其自动化学报,2002,14(5):1-3,24,33
[42] 岳蔚,刘沛.基于数学形态学消噪的电能质量扰动检测法.电力系统自动化,2002,26(7):13-17
[43] 王庆禹,褚福磊.小波变换中的能量泄漏问题.机械科学与技术,2001,20(1):12-13,16
[44] 张宇辉,陈晓东,王鸿懿.基于连续小波变换的电能质量测量与分类.电力自动化设备,2004,24(3):17-21
[45] 李天云,陈晓东,赵为红等.几种短时电能质量扰动分类和检测的双小波分析法.电力系统自动化,2003,27(22):26-29
[46] 刘安定,肖先勇,邓武军.短时电能质量扰动检测的一种新方法.继电器,2005,33(8):27-33
[47] 刘安定,肖先勇,邓武军.基于DCT/WT的电能质量扰动检测分析.电网技术,2005,29(10)
[48] Nara K, Hasegawa Oyama T, et, al. Forwarding to Future Power Delivery System. In: Proceeding of IEEE ICHQP Ⅸ. Orlando(USA): 2000, 8-18
[49] Dugan R C, McGranaghan M F, Beaty H W. Electrical Power System Quality. New York: McGraw-Hill, 1996
[50] 王成山,王继东.基于小波包分解的电能质量扰动分类方法.电网技术,2004,28(15):78-82
[51] 岳蔚,刘沛.基于数学形态学消噪的电能质量扰动检测方法.电力系统自动化,2002,26(7):13-17
[52] Hussain A, Sukairi M H, Mohamed A. Automatic detection of power quality disturbances and identification of transient signals. Proceedings of the Sixth International Symposium on Signal Processing and its Applications, 2001, 2(2): 462-465
[53] Poisson O, Rioual P, Meunier M. Detection and measurement of power quality disturbances using wavelet transform. IEEE transactions on Power Delivery, 2000, 15(3): 1039-1044
[54] 杨福生.小波变换的工程分析与应用.北京,科学出版社,1999
[55] Stephane Mallat. A Wavelet Tour of Signal Processing. BeiJing, China Machine Press, 2002
[56] Auscher P, Weiss G, Wickerhauser M V. Local Sine and Cosine Base of Coifman and Meyer and the Construction of Smooth Wavelet. Wavelets: A Tutorial in Theory and Application, Academic Press, 1992: 237-256
[57] Chen C T, Oonoho O. Atomic decomposition by basis pursuit. SPIE international Conference on Wavelet, San Diego, 1995
[58] Qiang C, Huang T S. Robust optimum detection of transform domain multiplicative watermarks. IEEE Transactions on Signal Processing, 2003, 51(4): 906-924
[59] Dong E, Zhao n M, Li Yongli. Low bit and variable rate speech coding using local cosine transform. 2002 IEEE Region 10 Annual International Conference on Computer, Communications, Control and Power Engineering, Proceedings, 2002, 1(1): 423-426
[60] Hamid E Y, Kawasaki Z L, Madiana R. Method for RMS and power measurements based on the wavelet packet transform. IEE Proceedings: Science, Measurement and Technology, 2002, 149(2): 60-66
[61] Meliopoulas A P S, Fardanesh B, Zelingher S. Harmonic measurement system via synchronized measurements. 2000 Power Engineering Society Summer Meeting, 2000, 2(2): 1094-1100