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研究生:范丙林
研究生(外文):Ping-Lin Fan
論文名稱:光電實驗曲線係數擬合之研究
論文名稱(外文):Study of Optoelectronic Experiments Coefficients Fitting
指導教授:張榮森張榮森引用關係
指導教授(外文):Rong-Seng Chang
學位類別:博士
校院名稱:國立中央大學
系所名稱:光電科學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:109
中文關鍵詞:係數擬合
外文關鍵詞:Coefficients fitting
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封面
Abstract
List of Tables
List of Figures
Acronym
Chapter 1 Introduction
1-1Background
1-2Motivation
1-2-1 Strain Effects on Self-Organized Quantum Dots
1-2-2 Transmission Lines Protection Scheme for Power System
1-2-3 Aberration Coefficients Fitting
1-3Chapter Outlines
Chapter 2 Numerical Methods
2-1Least Squares Methods
2-2Discrete Fourier Transform
2-3Wavelet Transform
2-4Dyadic Wavelet Transform
Chapter 3 Thickness-Dependent Renormalization of Strain Effects on Self-Organized InAs Quantum Dots grown on GaAs
3-1Experiments
3-2Results and Discussion
3-3Conclusion
Chapter 4 Fault Detection with PMU Based Approach and Dyadic Wavelet Transform for Transmission lines of Power System
4-1Part I: PMU Based Approach
4-1-1 Basic Principles
4-1-2 The Adaptive Protection Scheme
4-1-3 Performance Evaluation
4-2Part II: Dyadic Wavelet Transform Based Approach
4-2-1 Basic Ideas
4-2-2 Experiments with Simulated Waveforms
4-3Conclusion
Chapter 5 Aberration Coefficients Fitting by Using the Least Squares Method and the Wavelet Transform method
5-1Computing Aberration Coefficients by the Least-Squares Method
5-2Computing Aberration Coefficients by the Wavelet Transform
5-3Simulation Results
5-4Conclusion
Chapter 6  Summary and Future Works
6-1Summary
6-2Future Works
References
Tables
Figures
Appendix A
Appendix B


ReferencesChapter1.[1.1] L. Rabiner, B. Gold, ”Theory and Application of Digital Signal Procassing. Prentice Hall,1975.[1.2] D. DeFatta, J. Lucas and W. Hodgkiss, Digital Signal Processing: A System Design Approcah.John Wiley and Sons.1998.[1.3] A. Oppenheim and R, Schafer, Digital Signal Processing. Prentice Hall,1975.[1.4] T. J. Abatzoglou, J.M. Mendel and G.A. Harada, “The contrained total least squares technique and its applications to harmonic superresolution ,” IEEE Trans. Acoust.,Speech, Signal Processing, Vol ASSP-39, pp.1070-1087, May 1991.[1.5] K. S. Arun, ”A unitarily constrained total least squares problem in signal processing,” SIAM J. Matrix Anal., Vol.13, NO3, pp.729-745, July 1992.[1.6] G. H. Golub and C.F.Van Loan, ”An analysis of the total least squares problem,” SIAM J. Numer. Anal.,Vol.17, No.6, pp.883-893, Dec.1980.[1.7] S. M. Kay, Modern Spectral Estimation, Theory and Application, Englewood Cliffs: Prentice Hall ,1988.[1.8] G. W. Stewart, Introduction to Matrix Computations, New York: Academic Press, 1973.[1.9] A. A Girgis, ”A New Kalman Filtering-Based Digital Distance Relay”, IEEE Transaction on Power Apparatus and System, Vol. Pas-101, No.9, pp.3471-3479, September 1982.[1.10] T. akagi, Y. Yamakoshi, J. Baba, K. Uemura, and T. Sakaguchi, ’A New Alogrithm of an Accurate Fault Location for EHV/UHV Transmission Lines: Part I- Fourier Transformation Method”, IEEE Transactions on Power Apparatus and System,Vol. PAS-100, No.3, pp.1316-1323, March 1981.[1.11] T. Takagi, Y. Yamakoshi, J. Baba, K. Uemura, and T. Sakaguchi, ’A New Alogrithm of an Accurate Fault Location for EHV/UHV Transmission Lines:Part II-Lapace Transform Method”, IEEE Transsctions on Power Apparatus and System,Vol.PAS-101, No.3, pp.564-573, March 1982 .[1.12] M. Kezunovic, J. Mrkic, and B.Perunicic, ”An Accurate Fault Location Algorithm Using Synchronized Sampling”, Electric Power Systems Research, Vol.29, pp.161-169, 1994.[1.13] A. A Girbis, D. G. Hart, and W. L. Peterson, ”A New Fault Location Technique For Two-and Tree-Terminal Lines”, IEEE Transactions on Power Delivery, Vol.7, No.1, pp.98-107, January 1992.[1.14] D. Novosel, D. G. Hart, E. Udren, and J Garitty, ”Unsynchronized Two-Terminal Fault Location Estimation”, IEEE Transactions on Power Delivery, Vol.11, No.1, pp.130-137, January 1996.[1.15]A. T. John, and S. Jamali, ”Accurate Fault Locaton Technique For Power Transmission Lines”, IEE Proceedings, Vol.137, Pt.C, No, pp.395-402, November 1990.[1.16] P. K. Aggarwal, D. V. Coury, A. T. Johns, and A. Kalam, ”A Practical Approach to Accurate Fault Location on Extra High Voltage Teed Feeders”, IEEE Transactions on Power Delivery, Vol.8, No.3, pp.874-883, July 1992.[1.17] D. J. Lawrence, L. Z. Cabeza, and L. T. Hochberg, ”Development of an Advanced Transmission Line Fault Location, Part I: Input Transducer Analysis and Requirements”, IEEE Transactionson Power Delivery, Vol.7, No.4, pp.1963-1971, October 1992.[1.18] Z. Q. Bo, G. Weller, T. Lomas, and M. A. Redfern, “Positional Protection of Transmission Systems Using Global Positioning System”, IEEE Trans. on Power Delivery, Vol. 15, No. 4, pp. 1163-1168, October 2000.[1.19] R. K. Aggarwal and A. T. Johns, “A Differential Line Protection Scheme for Power Systems Based On Composite Voltage and Current Measurements”, IEEE Trans. on Power Delivery, Vol. 4, No. 3, pp. 1595-1601, July 1989.[1.20] H. Y. Li, E. P. Southern, P. A. Crossley, S. Potts, S. D. A. Pickering, B. R. J. Caunce and G. C. Weller, “A New Type of Differential Feeder Protection Relay Using the Global Positioning System for Data Synchronization”, IEEE Trans. on Power Delivery, vol. 12, no.3, pp. 1090-1097, July 1997.[1.21] J. A. Jiang, J. Z. Yang, Y. H. Lin, C. W. Liu, and J. C. Ma, “An Adaptive PMU Based Fault Detection/Location Technique for Transmission Lines, Part I: Theory and Algorithms”, IEEE Trans. on Power Delivery, vol. 15, no. 2, pp. 486-493, April 2000.[1.22] J. A. Jiang, Y. H. Lin, J. Z. Yang, T. M. Too, C. W. Liu, “An Adaptive PMU Based Fault Detection/Location Technique for Transmission Lines, Part II: PMU Implementation and Performance Evaluation”, IEEE Trans. on Power Delivery, vol. 15, no. 4, pp. 1136-1146, October 2000.[1.23] O. Chaari, M. Meunier, and F. Brouaye, “Wavelet: a New Tool for the Resonant Grounded Power Distribution Systems Relaying”, IEEE Trans. on Power Delivery, vol. 11, no.3, pp. 1301-1308, July 1997.[1.24] R.K.Martinet, J. Morlet, and A.Grossmann, “Analysis of sound patterns through wavelet transforms”, Int. J. Patt. Rec. Art. Intell.1,273-302(1987).[1.25] C. K. Chui, " Wavelet: A tutorial in theory and application," Academic Press, 1991.[1.26] P. Delsing, T. Claeson, G. S. Kazacha, L. S. Kuzmin, and K. K. Likharev, “ 1-D array implementation of the resistively- couple single-electron transistor,” IEEE Trans. Magn. Vol. 27, No. 2, March,1991[1.27] C. Wasshuber, H, Kosina, S. Siegfried, “A comparative study of single-electron memoroes”, IEEE Trans. Electron Devices, vol. 45, NO. 11, Nov. 1998. [1.28] D. Pan and E. Towe, “A five-period normal-incidence (In, Ga)As/GaAs quantum-dot infrared photodector,” Appl. Phys. Lett. 75, 2079 (1999).[1.29] Yu. M. Shernyakov et. al., “1.3 μm GaAs-based laser using quantum dots obtained by activated spinnodal decomposition,” Electron. Lett., 35, (11), pp. 898-900. [1.30] A. Passaseo, G. Maruccio, M. De Vittorio, R. Rinaldi, and R. Cingolani, “Wavelength control from 1.25 to 1.4 μm in InxGa1-xAs quantum dot structures grown by metal chemical vapor deposition,” Appl. Phys. Lett. 78, 1382 (2001).[1.32] J. Tatebayashi, M. Nishioka, and Y. Arakawa, “Over 1.5 μm light emission from InAs quantum dots embedded in InGaAs strain-reducing layer grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 78, 3469 (2001).[1.33] V. M. Ustinov, N. A. Maleev, A. E. Zhukov, A. R. Kovsh, A. Yu. Egorov, A. V. Lunve, B. V. Volovik, I. L. Krestnikov, Yu. G. Musikhin, N. A. Bert, P. S. Kop’ev, Zh. I. Alferov, N. N. Ledentsov, and D. Bimberg, “InAs/InGaAs quantum dot structures on GaAs substrates emitting 1.3 μm ,” Appl. Phys. Lett. 74, 2815 (1999).[1.34] M. Sopanen, H. P. Xin, and C. W. Tu, “Self-assembled GaInNAs quantum dot structures for 1.3 and 1.5 μm emission on GaAs,” Appl. Phys. Lett. 76, 994 (2000).[1.35] K. Nishi, H. Saito, and J.-S. Lee, “ A narrow photoluminescence linewidth of 21 meV at 1.35μm from strain-reduced InAs quantum dots cover by In0.2Ga0.8As grown on GaAs substrates,”Appl. Phys. Lett. 74, 1111 (1999).[1.36] J. Bloch, J. Shah, W. S. Hobson, and J. Lopata, “ Optical properties of multiple layers of self-organized InAs quantum dots emitting at 1.3 μm ,” Appl. Phys. Lett. 77, 2545 (2000).[1.37] K. Mukai and M. Sugawara, “Suppression of temperature sensitivity of interband emission energy in 1.3-μm-region by an InAsGa overgrowth on self-assembled InGaAs/GaAs quantum dots,” Appl. Phys. Lett. 74, 3963 (1999).[1.38] A. G. Phadke and J. S. Thorp, Computer Relaying for Power Systems, John Wiley & Sons, New York, 1988.[1.38] Working Group H-7 of the Relaying Channels Subcommittee of the IEEE Power System Relaying Committee, “Synchronized Sampling and Phasor Measurements for Relaying and Control”, IEEE Trans. on Power Delivery, vol. 9, no. 1, pp. 442-452, January 1994.[1.39] A. A. Girgis and E. B. Makram, “Application of Adaptive Kalman Filtering in Fault Classification, Distance Protection, and Fault Location Using Microprocessors”, IEEE Trans. on Power Systems, Vol. 3, No. 1, pp. 301-309, February 1988.[1.40] D. V. Coury and D. C. Jorge, “Artificial Neural Network Approach to Distance Protection of Transmission Lines”, IEEE Trans. on Power Delivery, Vol. 13, No. 1, pp. 102-108, January 1998.[1.41] T. S. Sidhu, H. Singh, and M. S. Sachdev, “Design, Implementation and Testing of An Artificial Neural Network Based Fault Direction Discriminator for Protecting Transmission Lines”, IEEE Trans. on Power Delivery, Vol. 10, No. 2, pp. 697-706, April 1995.[1.42] M. Akke and J. S Thorp, “Some Improvements In the Three-Phase Differential Equation Algorithm for Fast Transmission Line Protection”, IEEE Trans. on Power Delivery, vol. 13, no. 1, pp. 66-72, January 1998.[1.43] M. M. Mansour and G. W. Swift, “A Multi-Microprocessor Based Traveling Wave Relay - Theory and Realization”, IEEE Trans. on Power Delivery, Vol. 1, No. 1, pp. 272-279, January 1986.[1.44] Z. Q. Bo, G. Weller, T. Lomas, and M. A. Redfern, “Positional Protection of Transmission Systems Using Global Positioning System”, IEEE Trans. on Power Delivery, Vol. 15, No. 4, pp. 1163-1168, October 2000.[1.45] R. K. Aggarwal and A. T. Johns, “A Differential Line Protection Scheme for Power Systems Based On Composite Voltage and Current Measurements”, IEEE Trans. on Power Delivery, Vol. 4, No. 3, pp. 1595-1601, July 1989.[1.46] H. Y. Li, E. P. Southern, P. A. Crossley, S. Potts, S. D. A. Pickering, B. R. J. Caunce and G. C. Weller, “A New Type of Differential Feeder Protection Relay Using the Global Positioning System for Data Synchronization”, IEEE Trans. on Power Delivery, vol. 12, no.3, pp. 1090-1097, July 1997.[1.47] J. A. Jiang, J. Z. Yang, Y. H. Lin, C. W. Liu, and J. C. Ma, “An Adaptive PMU Based Fault Detection/Location Technique for Transmission Lines, Part I: Theory and Algorithms”, IEEE Trans. on Power Delivery, vol. 15, no. 2, pp. 486-493, April 2000.[1.48] J. A. Jiang, Y. H. Lin, J. Z. Yang, T. M. Too, C. W. Liu, “An Adaptive PMU Based Fault Detection/Location Technique for Transmission Lines, Part II: PMU Implementation and Performance Evaluation”, IEEE Trans. on Power Delivery, vol. 15, no. 4, pp. 1136-1146, October 2000.[1.49] “Alternative Transient Program Rule Book”, Vol. 1, X. U. Leuven Center, July 1987.[1.50] S.Santoso, E. J. Powers, and P. Hofmann, “Power quality assesment via wavelet transform analysis,” IEEE Trans. on Power Delivery, vol. 11, No 2, pp. 924-930, Apr. 1996.[1.51 ] P. Pillay, and A. Bhattacharjee,”Application of wavelets to model short term power system disturbances,” IEEE Trans. on Power System, vol. 11, No 4, pp.2031-2037, November 1996.[1.52] M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), Sec.9.2.[1.53] F. Zernike, “Beugungstheorie des Schnridenver-Eahrens und Seiner Verbesserten Form, der Phasenkontrastmethode,” Physica 1, 689 (1934).[1.54] D. Malacara, J. M. Carpio-Valad`ez, and J. J.S`anchez-Mondrag`on, “ Wave-front fitting with discrete orthogonal polynomials in a unit radius circle,” Opt. Eng. 29, 672-675 (1990).[1-55] J. Y. Wang and D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510-1518 (1980).[1-56] E. Freysz, B. Pouligny. F. Argoul, and A. Arneodo, “Optical wavelet transform of fractal aggregatet,” Phys. Rev. Lett.64, 7745-7748(1990).[1-57] R.K.Martinet, J.Morlet, and A.Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Patt. Rec Art.Intell.1,273-302(1987).[1.58] H. J. Caufield, “Wavelet transforms and their relatives, ” Photon. Spectra 26,73(1992).[1-59] J. M. Combes, A. Grossmann, and Ph. Tchamitchian, eds.,Wavelets: Time-Frequency Methods and Phase Space (Springer-Verlag.Berlin, 1989).[1.60] G. E. Forsythe, J. Soc. Ind. Math. 5, 74(1957).[1.61] Daubechies, “The wavelet transform time-frequency localization and signal analysis, ” IEEE Trans.Inf. Theory 36,961-1005(1990).Chapter 2.[2.1] R. L. Burden and J.D.Faires, Nmerical Analysis, Brooks/Cole, 1997.[2.2] A. G. Phadke and J. S. Thorp, Computer Relaying for Power Systems, John Wiley & Sons, New York, 1988.[2.3] C. S. Burrus, R. A. Gopinath, and H.T. Guo, Introduction to Wavelets and Wavelet transform, Prentic Hall Press,1998.[2.4] X. Zhang, J. Zheng, and H. Gao, “Curve fitting using wavelet transform for resolving simulated overlapped spectra”, Analytica Chimica Acta 443(2001) P117-125.Chapter 3.[3.1] A. Passaseo, G. Maruccio, M. De Vittorio, R. Rinaldi, and R. Cingolani, “Wavelength control from 1.25 to 1.4 μm in InxGa1-xAs quantum dot structures grown by metal chemical vapor deposition,” Appl. Phys. Lett. 78, 1382 (2001).[3.2] J. Tatebayashi, M. Nishioka, and Y. Arakawa, “Over 1.5 μm light emission from InAs quantum dots embedded in InGaAs strain-reducing layer grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 78, 3469 (2001).[3.3] V. M. Ustinov, N. A. Maleev, A. E. Zhukov, A. R. Kovsh, A. Yu. Egorov, A. V. Lunve, B. V. Volovik, I. L. Krestnikov, Yu. G. Musikhin, N. A. Bert, P. S. Kop’ev, Zh. I. Alferov, N. N. Ledentsov, and D. Bimberg, “InAs/InGaAs quantum dot structures on GaAs substrates emitting 1.3 μm ,” Appl. Phys. Lett. 74, 2815 (1999).[3.4] M. Sopanen, H. P. Xin, and C. W. Tu, “Self-assembled GaInNAs quantum dot structures for 1.3 and 1.5 μm emission on GaAs,” Appl. Phys. Lett. 76, 994 (2000).[3.5] K. Nishi, H. Saito, and J.-S. Lee, “ A narrow photoluminescence linewidth of 21 meV at 1.35μm from strain-reduced InAs quantum dots cover by In0.2Ga0.8As grown on GaAs substrates,” Appl. Phys. Lett. 74, 1111 (1999).[3.6] J. Bloch, J. Shah, W. S. Hobson, and J. Lopata, “ Optical properties of multiple layers of self-organized InAs quantum dots emitting at 1.3 μm ,” Appl. Phys. Lett. 77, 2545 (2000).[3.7] K. Mukai and M. Sugawara, “ Suppression of temperature sensitivity of interband emission energy in 1.3-μm-region by an InAsGa overgrowth on self-assembled InGaAs/GaAs quantum dots,” Appl. Phys. Lett. 74, 3963 (1999).[3.8] For the InAs and GaAs deformation potential parameters we used a(eV; InAs) = -6.08; a(eV; GaAs) = -8.33; b(eV; InAs) = -1.8; b(eV; GaAs) = -1.7; C11(InAs) = 8.329; C12(1011dyne/cm2; InAs) = 4.526; C11(1011dyne/cm2; GaAs) = 11.879; C12(1011dyne/cm2; GaAs) = 5.376; K. H. Hellwege, Ed., Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology, New Series, Group III 17a, Springer, Berlin, (1982); Groups III-V 22a, Springer, Berlin, (1986).[3.9] E. Pehlke, N. Moll, A. Kely, and M. Scheffler, “ Shape and stability of quantum dot, ” App. Phys. A 65, 525 (1997).[3.10] M. Grundmann, O. Stier, and D. Bimberg, “ InAs/GaAs pyramidal quantum dots: Strain distribution, optical phonos, and electronic structure,” Phys. Rev. B52, 11969 (1995).[3.11] R. M. Lin, T. E. Nee, M. C. Tsai, Y. H Chang, P. L. Fan and R. S. Chang, “ Thickness-dependent renormalization of strain effects on self-organized InAs quantum dots grown on GaAs,” J. Vac. Sci. Technol. A 20(3), May/Jun 2002.Chapter 4.[4.1] A. G. Phadke and J. S. Thorp, Computer Relaying for Power Systems, John Wiley & Sons, New York, 1988.[4.2] Working Group H-7 of the Relaying Channels Subcommittee of the IEEE Power System Relaying Committee, “Synchronized Sampling and Phasor Measurements for Relaying and Control”, IEEE Trans. on Power Delivery, vol. 9, no. 1, pp. 442-452, January 1994.[4.3] A. A. Girgis and E. B. Makram, “Application of Adaptive Kalman Filtering in Fault Classification, Distance Protection, and Fault Location Using Microprocessors”, IEEE Trans. on Power Systems, Vol. 3, No. 1, pp. 301-309, February 1988.[4.4] D. V. Coury and D. C. Jorge, “Artificial Neural Network Approach to Distance Protection of Transmission Lines”, IEEE Trans. on Power Delivery, Vol. 13, No. 1, pp. 102-108, January 1998.[4.5] T. S. Sidhu, H. Singh, and M. S. Sachdev, “Design, Implementation and Testing of An Artificial Neural Network Based Fault Direction Discriminator for Protecting Transmission Lines”, IEEE Trans. on Power Delivery, Vol. 10, No. 2, pp. 697-706, April 1995.[4.6] M. Akke and J. S Thorp, “Some Improvements In the Three-Phase Differential Equation Algorithm for Fast Transmission Line Protection”, IEEE Trans. on Power Delivery, vol. 13, no. 1, pp. 66-72, January 1998.[4.7] M. M. Mansour and G. W. Swift, “A Multi-Microprocessor Based Traveling Wave Relay - Theory and Realization”, IEEE Trans. on Power Delivery, Vol. 1, No. 1, pp. 272-279, January 1986.[4.8] Z. Q. Bo, G. Weller, T. Lomas, and M. A. Redfern, “Positional Protection of Transmission Systems Using Global Positioning System”, IEEE Trans. on Power Delivery, Vol. 15, No. 4, pp. 1163-1168, October 2000.[4.9] R. K. Aggarwal and A. T. Johns, “A Differential Line Protection Scheme for Power Systems Based On Composite Voltage and Current Measurements”, IEEE Trans. on Power Delivery, Vol. 4, No. 3, pp. 1595-1601, July 1989.[4.10] H. Y. Li, E. P. Southern, P. A. Crossley, S. Potts, S. D. A. Pickering, B. R. J. Caunce and G. C. Weller, “A New Type of Differential Feeder Protection Relay Using the Global Positioning System for Data Synchronization”, IEEE Trans. on Power Delivery, vol. 12, no.3, pp. 1090-1097, July 1997.[4.11] J. A. Jiang, J. Z. Yang, Y. H. Lin, C. W. Liu, and J. C. Ma, “An Adaptive PMU Based Fault Detection/Location Technique for Transmission Lines, Part I: Theory and Algorithms”, IEEE Trans. on Power Delivery, vol. 15, no. 2, pp. 486-493, April 2000.[4.12] J. A. Jiang, Y. H. Lin, J. Z. Yang, T. M. Too, C. W. Liu, “An Adaptive PMU Based Fault Detection/Location Technique for Transmission Lines, Part II: PMU Implementation and Performance Evaluation”, IEEE Trans. on Power Delivery, vol. 15, no. 4, pp. 1136-1146, October 2000.[4.13] “Alternative Transient Program Rule Book”, Vol. 1, X. U. Leuven Center, July 1987.[4.14] S.Santoso, E. J. Powers, and P. Hofmann, “Power quality assesment via wavelet transform analysis,” IEEE Trans. on Power Delivery, vol. 11, No 2, pp. 924-930, Apr. 1996.[4.15 ] P. Pillay, and A. Bhattacharjee,”Application of wavelets to model short term power system disturbances,” IEEE Trans. on Power System, vol. 11, No 4, pp.2031-2037, November 1996.[4.16] G. T. Heydt, and A.W. Galli,”Power quality problem analyzed using wavelets,” IEEE Trans. on Power Systems, vol. 12, No 2, pp.869-915, Apr. 1997.[4.17] T. B. Littler, and D. J. Morrow, ”Wavelets for the analysis of power system disturbances,” IEEE Trans. on Power Delivery, vol.14, No 4, pp.358-364, Apr. 1999.[4.18] S. Huang, C. Hsieh, and C. Lien Huang,” Application of Morlet wavelets to supervise power system disturbances,” IEEE Trans. on Power Delivery, vol. 14, No 1, pp.235-243, January 1999.[4.19] A.W. Galli, and O.M. Nielsen,” Wavelet analysis for power systems transients,” IEEE Computer Applications in Power, pp.16-25, January 1999.Chapter 5.[5.1] M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), Sec.9.2.[5.2] F. Zernike, “Beugungstheorie des Schnridenver-Eahrens und Seiner Verbesserten Form, der Phasenkontrastmethode,” Physica 1, 689 (1934).[5.3] D. Malacara, J. M. Carpio-Valad`ez, and J. J. S`anchez-Mondrag`on, “ Wave-front fitting with discrete orthogonal polynomials in a unit radius circle,” Opt. Eng. 29, 672- 675 (1990).[5.4] J. Y. Wang and D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510-1518 (1980).[5.5] E. Freysz, B. Pouligny. F. Argoul, and A. Arneodo,“Optical wavelet transform of fractal aggregatet,” Phys. Rev. Lett. 64, 7745-7748 (1990).[5.6] R. K. Martinet, J.Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Patt. Rec Art. Intell. 1, 273-302 (1987).[5.7] H. J. Caufield, “Wavelet transforms and their relatives,” Photon. Spectra 26,73(1992).[5.8] J. M. Combes, A. Grossmann, and Ph. Tchamitchian, eds., Wavelets: Time-Frequency Methods and Phase Space (Springer-Verlag.Berlin, 1989).[5.9] G. E. Forsythe, J. Soc. Ind. Math. 5, 74 (1957).[5.10] Daubechies, “The wavelet transform time-frequency localization and signal analysis, ” IEEE Trans. Inf. Theory, 36, 961-1005 (1990).[5.11] H. Szu, Y. Sheng, and J. Chen, “The wavelet transform as a bank of matched filters, ” Appl. Opt. 31, 3267-3277 (1992).[5.12] Y. Sheng, D. Roberge, and H. Szu, “Optical wavelet transform, ” Opt. Eng. 31, 1840-1845 (1992).[5.13] D. Marr, E. Hildreth, Proc. Royal Soc. London B 207 (1980).[5.14] Wavelet Toolbox For Use with MATLAB (The Math Works, Inc, 1997).

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