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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 貝蘇章 | |
| dc.contributor.author | Ya-Tin Fan | en |
| dc.contributor.author | 范雅婷 | zh_TW |
| dc.date.accessioned | 2021-06-08T06:09:34Z | - |
| dc.date.copyright | 2007-07-27 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-11 | |
| dc.identifier.citation | [1] Merrill I. Skolnik, Introduction to Radar Systems, Mcgraw-Hill College (1980)
[2] Gene F., J. David Powell, and Michael L. Workman Franklin, Digital Control of Dynamic Systems, Addison-Wesley (1980), Second Edition [3] Rafael C. Gonzalez, Richard E. Woods, Digital Image Processing, Addison-Wesley Pub (Sd) (1992) [4] Tompkins, Design of Microcomputer-Based Medical Instrumentation, Prentice Hall (January 1981) [5] M. A. Al-Alauoi, Novel approach to designing digital differentiators, Electron. Letter, vol. 28, no. 15, pp. 1376-1378, Jul. 1992 [6] M. A. Al-Alauoi, Novel digital integrator and differentiator, Electron. Letter, vol. 29, no. 4, pp. 376-378, Feb. 1993 [7] M. A. Al-Alauoi, Novel IIR differentiator from the Simpson integration rule, IEEE Trans. Circuits and Systems—I: Fundam. Theory Appl., vol. 41, no. 2, pp. 186-187, Feb. 1994 [8] Steven C. Chapra, Applied numerical methods with MATLAB for engineers and scientists, McGraw-Hill [9] S. C. Chapra and R. P. Canale, Numerical Methods for Enginneers, 2nd ed. Singapore: McGraw-Hill, 1989 [10] John H. Mathews and Kurtis K. Fink, Numerical Methods Using Matlab, 4th Edition, Prentice-Hall Inc., 2004 [11] Chien-Cheng Tseng, Closed-Form Design of Digital IIR Integrators Using Numerical Integration Rules and Fractional Sample Delays, IEEE Trans. Circuits and Systems—I: Fundam. Theory Appl., vol.54, pp. 643-655, Mar. 2007 [12] T. I. Laakso, V. Valimaki, M. Karjalainen and U.K. Laine, Splitting the unit delay: tool for fractional delay filter design, IEEE Signal Processing Magazine, pp.30-60, Jan. 1996. [13] Chien-Cheng Tseng, Digital integrator design using Simpson rule and fractional delay filter, IEE Proc. Vision, Image and Signal Proc., vol.153, pp. 79-86, Feb. 2006 [14] M. M. Chawla, Error Estimates for the Clenshaw-Curtis Quadrature, Mathematics of Computation, vol. 22, no. 103, pp. 651-656, Jul. 1968 [15] W. Morven Gentalman, Implementing Clenshaw-Curtis Quadrature, I Methodology and Experience, Comm. Of the ACM, vol. 15, no.5, May 1972 [16] Lloyd N. Trefethen, Is Gauss quadrature better than Clenshaw-Curtis? preprint (2006). [17] C. W. Clenshaw and A. R. Curtis, A method for numerical integration on an automatic computer, Numerische Mathematik, vol. 2, pp. 197-205, Dec. 1960 [18] Ramiro S. Barbosa, J. A. Tenreiro Machado, and Manuel F. Silva, Time domain design of fractional differintegrators using least-squares, Signal Processing, vol.86, pp. 2567-2581, 2006 [19] Y.Q. Chen, K.L. Moore, Discretization schemes for fractional-order differentiators and integrators, IEEE Trans. Circuits and Systems—I: Fundam. Theory Appl., vol. 49, no. 3, pp.363-367, Mar. 2002 [20] B. M. Vinagre, I. Podlubny, A. Hernandez, V. Feliu, Some approximations of fractional order operators used in control theory and applications, Fractional Calculus & Applied Analysis, vol. 3, no. 3, pp. 945-950, 2000 [21] Chien-Cheng Tseng, Improved design of digital fractional-order differentiators using fractional sample delay, IEEE Trans. Circuits and Systems—I: Fundam. Theory Appl., vol.53, pp.193-203, Jan. 2006 [22] Quoc Ngo, A New Approach for the Design of Wideband Digital Integrator and Differentiator, IEEE Trans. Circuits and Systems—II: Express Briefs, vol. 53, no. 9, pp. 936-940, Sept. 2006 [23] Chien-Cheng Tseng, Design of variable and adaptive fractional order FIR differentiators, Signal Processing, vol.86, pp. 2554-2566, 2006 [24] Chien-Cheng Tseng, Design of FIR and IIR fractional order Simpson digital integrators, Signal Processing, vol.87, pp. 1045-1057, 2007 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/25337 | - |
| dc.description.abstract | 本文介紹一些常見的數位微積分器及分數階微積分器。第二到四章介紹三種積分的數值方：Newton-Cotes quadrature rule, Gauss-Legendre quadrature rule 和 Clenshaw-Curtis quadrature rule。伴隨這些數值方而來的小數週期元件就利用一些已熟知的小數週期延遲濾波器，例如: FIR Lagrange 和IIR allpass fractional delay filters來做IIR數位積分器的設計。我們用圖形比較以上設計的優缺點並提出一個合併的設計。第五章我們用一系列的方法來設計分數階微積分器。先是比較一些連續輸入數位化， 轉換的方法；其次利用二項展開或連分數展開，使得分數階可以化成整數階。利用最小平方誤差的方法來降低錯誤率。我們比較不同方法的頻率響應上的錯誤率以及在相位上的表現。並且，我們討論這些濾波器的特性。最後第六章，我們做一些整理和建議未來可以繼續研究的方向。 | zh_TW |
| dc.description.abstract | In this thesis, we introduce a few designs of digital integrator, and a few designs of fractional-order differintegrator. We apply some numerical integration rules and fractional delay filters to obtain the closed form design of IIR digital integrators. There are three types of numerical integration rules to be investigated: Newton-Cotes quadrature rule, Gauss-Legendre quadrature rule and Clenshaw-Curtis quadrature rule. The fractional delay involved in the design will be implemented by FIR Lagrange and IIR allpass fractional delay filters. Also, a combined version is proposed. Several digital filter design examples are illustrated to demonstrate the effectiveness. Chapter 5 is to show the designs of the fractional-order differintegrator. We find a suitable generating function to fit the ideal fractional-order differintegrator. Then discretize the fractional-order with a power series expansion or continued fraction expansion. Last, we discuss the different methods to decrease the absolute magnitude error. Moreover, the filter properties will also be presented at the end of the chapter. Finally, we make a conclusion of this thesis and suggest the future work in chapter 6. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T06:09:34Z (GMT). No. of bitstreams: 1 ntu-96-R94942107-1.pdf: 542641 bytes, checksum: 0d00e53bcef011793bf27e9128ca53a6 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | Chapter 1 Introduction 1
Chapter 2 Digital Integrator Design Using Newton-Cotes Quadrature Rules 5 2.1 Introduction 5 2.2 Newton-Cotes quadrature rules 6 2.3 Design using Newton-Cotes quadrature rules 7 2.3.1 Use Newton-Cotes quadrature rules to design IIR filters based on the same sampling period T 8 2.3.2 Use Newton-Cotes quadrature rules to design IIR filters based fixed end points 9 2.4 Implementation 12 2.4.1 FIR Lagrange filter approximation 12 2.4.2 IIR allpass filter approximation 14 2.4.3 Combined approximation 17 2.5 Conclusion 20 Chapter 3 Digital Integrator Design Using Gauss-Legendre Quadrature Rules 21 3.1 Introduction 21 3.2 Gauss-Legendre quadrature rules 22 3.3 Design using Gauss-Legendre quadrature rules 23 3.4 Implementation 28 3.5 Conclusion 30 Chapter 4 Digital Integrator Design Using Clenshaw-Curtis Quadrature rules 31 4.1 Introduction 31 4.2 Design using Clenshaw-Curtis quadrature rules 32 4.3 Implementation 35 4.4 Conclusion and Comparison 37 Chapter 5 Fractional-order Differintegrator Design 39 5.1 Introduction 39 5.2 Design of FIR approximation to fractional differintegrators using power series expansion 40 5.3 Design of FIR approximation to fractional differintegrators using fractional delay filter 45 5.4 Design IIR fractional-order differintegrator using continued fraction expansion 48 5.5 Design of IIR approximations to fractional differintegrators using least square error 53 5.5.1 Some approximation schemes 54 A. Padé approximation 54 B. Prony’s method 55 C. Shanks’ method 56 5.5.2 Experimental result 57 5.6 Conclusion 60 Chapter 6 Conclusion and Future Work 63 Reference 65 | |
| dc.language.iso | en | |
| dc.title | 數位分數階微分器及積分器之設計 | zh_TW |
| dc.title | The Design of Digital Fractional-order Differentiators and Integrators | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李枝宏,徐忠枝 | |
| dc.subject.keyword | 數位積分器,數值積分法,分數階微積分器,數位化,數位微分器,連分數展開, | zh_TW |
| dc.subject.keyword | Digital integrator,Numerical integration rule,fractional-order differintegrator,Discretization,Digital differentiator,Continued fraction expansion, | en |
| dc.relation.page | 68 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2007-07-14 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 電信工程學研究所 | zh_TW |
| 顯示於系所單位： | 電信工程學研究所 | |
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