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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 貝蘇章 | |
| dc.contributor.author | Bo-Yi Guo | en |
| dc.contributor.author | 郭柏毅 | zh_TW |
| dc.date.accessioned | 2021-06-08T02:38:34Z | - |
| dc.date.copyright | 2018-08-01 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2018-07-17 | |
| dc.identifier.citation | Chapter 1
[1.1] D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega and P. Vandergheynst, “The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains,” IEEE Signal Process. Mag., vol. 30, no. 3, pp.83–98, May 2013. [1.2] F. Zhang and E. R. Hancock, “Graph spectral image smoothing using the heat kernel,” Pattern Recognit., vol. 41, pp. 3328–3342, Nov. 2008. [1.3] S. K. Narang, Y. H. Chao, and A. Ortega, “Graph-wavelet filterbanks for edge-aware image processing,” in Proc. IEEE Stat. Signal Process. Workshop, Ann Arbor, MI, Aug. 2012, pp. 141–144. [1.4] S.-C. Pei, W.-S. Lu and C.-C. Tseng, “Analytical two-dimensional IIR notch filter design using outer product expansion,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 44, no. 9, pp. 765-768, Sept. 1997. [1.5] C.-C. Tseng and S.-C. Pei, “2D multiple notch filter design,” Electron. Lett., vol. 32, no. 22, pp. 2065-2066, Oct. 1996. [1.6] J. E. Cousseau, S. 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Mag., vol. 30, no. 3, pp.83–98, May 2013. [2.3] S. K. Narang, Y. H. Chao, and A. Ortega, “Graph-wavelet filterbanks for edge-aware image processing,” in Proc. IEEE Stat. Signal Process. Workshop, Ann Arbor, MI, Aug. 2012, pp. 141–144. [2.4] Z. Zhang, “Parameter estimation techniques: A tutorial with application to conic fitting,” Image and Vision Computing 15(1), 59–76 1997. [2.5] L. J. Grady and J. R. Polimeni, Discrete calculus: Applied analysis on graphs for computational science, Berlin, Germany: Springer, 2010. [2.6] L. Grady and M.-P. Jolly, “Weights and topology: A study of the effects of graph construction on 3D image segmentation,” in Proc. Int. Conf. Medical Image Computing and Computer Assisted Intervention, 2008, vol. 1, pp. 153–161. [2.7] M.J. Black, G. Sapiro, D.H. Marimont and D. Heeger, 'Robust Anisotropic Diffusion,' IEEE Trans. Image Processing, vol. 7, pp. 421-432, 1998. [2.8] F. K. Chung, Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, vol. 92). Providence, RI: AMS Bookstore, 1997. [2.9] A.V. Oppenheim, A.S. Willsky, S.H. Nawab, Signals and Systems, 2nd ed. Prentice Hall, 1997. [2.10] S. Chen, R. Varma, A. Sandryhaila and J. Kovačević, “Discrete signal processing on graphs: Sampling theory,” IEEE Trans. Signal Process., vol. 63, no. 24, pp. 6510-6523, 2015. [2.11] I. Pesenson, “Sampling in Paley-Wiener spaces on combinatorial graphs,” Trans. Amer. Math. Soc., vol. 360, no. 10, pp. 5603–5627, 2008. [2.12] X. Wang, P. Liu and Y. Gu, 'Local-set-based graph signal reconstruction', IEEE Trans. Signal Process., vol. 63, no. 9, pp. 2432-2444, 2015. [2.13] D. I Shuman, B. Ricaud, and P. Vandergheynst, “A windowed graph Fourier transform,” in Proc. IEEE Stat. Signal Process. Workshop, Ann Arbor, MI, Aug. 2012, pp. 133–136. [2.14] B. Girault, P. Goncalves, and E. Fleury, “Translation on graphs: an isometric shift operator,” IEEE Signal Processing Letters, vol. 22, no. 12, pp. 2416–2420, 2015. [2.15] M. Belkin and P. Niyogi, “Towards a theoretical foundation for Laplacian-based manifold methods,” J. Comput. Syst. Sci., vol. 74, no. 8, pp.1289–1308, 2008. [2.16] A. Sandryhaila and J. M. F. Moura, “Discrete signal processing on graphs,” IEEE Trans. Signal Process., vol. 61, no. 7, pp. 1644–1656, 2013. [2.17] Shi Xuesong, Feng Hui and Zhai Muyuan, 'Infinite Impulse Response Graph Filters in Wireless Sensor Networks', IEEE Signal Processing Letters, vol. 22, no. 8, pp. 1113-1117, 2015. [2.18] David B. H. Tay and Jingxin Zhang, “Techniques for Constructing Biorthogonal Bipartite Graph Filter Banks,” IEEE Trans. Signal Process., vol. 63, no. 21, pp. 5772–5783, 2015. [2.19] N. Perraudin, J. Paratte, D. I. Shuman, V. Kalofolias, P. Vandergheynst, and D. K. Hammond, “GSPBOX: A toolbox for signal processing on graphs,” Aug. 2014 [Online]. Available: http://arxiv.org/abs/1408.5781 Chapter 3 [3.1] F. Zhang, E.R. Hancock, “Graph spectral image smoothing using the heat kernel,” Pattern Recognit., vol. 41, no. 11, pp. 3328-3342, Nov. 2008. [3.2] S. K. Narang, G. Shen and A. Ortega “Unidirectional graph-based wavelet transforms for efficient data gathering in sensor networks,” in IEEE Int. Conf. Acoustics Speech and Signal Processing, Dallas, Mar. 2010, pp. 2902-2905. [3.3] S. K. Narang, A. Gadde, and A. Ortega, “Signal processing techniques for interpolation in graph structured data,” in IEEE Int. Conf. Acoustics Speech and Signal Processing, Vancouver, May 2013, pp. 5445-5449. [3.4] S. Chen, R. Varma, A. Sandryhaila, and J. Kovačević, “Discrete signal processing on graphs: Sampling theory,” IEEE Trans. Signal Process., vol. 63, no. 24, pp. 6510-6523, Aug. 2015. [3.5] P. Liu, X. Wang and Y. Gu, “Coarsening graph signal with spectral invariance,” in IEEE Int. Conf. Acoustics Speech and Signal Processing, Florence, May 2014, pp. 1070-1074. [3.6] A. Agaskar and Y. M. Lu, “A spectral graph uncertainty principle,” IEEE Trans. Inf. Theory, vol. 59, no. 7, pp. 4338-4356, Mar. 2013. [3.7] D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega and P. Vandergheynst, “The emerging field of signal processing on graphs,” IEEE Signal Process. Mag., vol. 30, no. 3, pp.83-98, May 2013. [3.8] A. Sandryhaila and J. M. F. Moura, “Discrete signal processing on graphs: Frequency analysis,” IEEE Trans. Signal Process., vol. 62, no. 12, pp. 3042-3054, Jun. 2014. [3.9] G. Karypis and V. Kumar, “A fast and high quality multilevel scheme for partitioning irregular graphs,” SIAM Journal on Scientific Computing, vol. 20, no. 1, pp. 359-392, Jan. 1998. [3.10] P Erdös, A Rényi, “On random graphs I,” Publications Mathematicae (Debrecen), vol. 6, pp. 290–297, 1959. Chapter 4 [4.1] S.-C. Pei and C.-C. Tseng, “Elimination of AC interference in electrocardiogram using IIR notch filter with transient suppression,” IEEE Trans. Biomed. Eng., vol. 42, no. 11, pp. 1128–1132, Nov. 1995. [4.2] I. Claesson and A. Rossholm, “Notch filtering of humming GSM mobile telephone noise,” in Proc. Int. Conf. Information, Communication and Signal Processing, 2005, pp. 1320–1323. [4.3] S.-C. Pei and C.-C. Tseng, “Two dimensional IIR digital notch filter design,” IEEE Trans. Circuits Syst. I, vol. 41, no. 3, pp. 227–231, Mar. 1994. [4.4] S.-C. Pei, W.-S. Lu, and C.-C. Tseng, “Two dimensional FIR notch filter design using singular value decomposition,” IEEE Trans. Circuits Syst. II, vol. 45, no. 3, pp. 290–294, Mar. 1998. [4.5] L. B. Milstein, “Interference rejection techniques in spread spectrum communications,” Proc. IEEE, vol. 76, no. 6, pp. 657–671, June 1988. [4.6] C.-C. Tseng and S.-C. Pei, “Stable IIR notch filter design with optimal pole placement,” IEEE Trans. Signal Processing, vol. 49, no. 11, pp. 2673-2681, Nov. 2001. [4.7] S.-C. Pei, B.-Y. Guo, W.-Y. Lu, G. E. Sobelman, and Y.-D. Huang, “Improved design of digital 1-D and 2-D notch filters using general feed- back structure,” in Proc. IEEE ISCAS, Montreal, QC, Canada, May 2016, pp. 2182–2185. [4.8] Y-D. Huang, “Design and Implementation of One-Dimensional and Multi-Dimensional Variable Digital Filters,” PhD Thesis, National Taiwan University, 2015. [4.9] S.-C. Pei, B.-Y. Guo, and W.-Y. Lu, “Narrowband notch filter using feedback structure,” IEEE Signal Process. Mag., vol. 33, no. 3, pp. 115–118, May 2016. [4.10] S. Engelberg, “Precise variable-Q filter design,” IEEE Signal Processing Mag., vol. 25, no. 5, pp. 113–119, Sept. 2008. [4.11] T. Li, J. Jiang, and L. Wang, “Pole-radius-varying IIR notch filter with transient suppression,” IEEE Trans. Instrum. Meas., vol. 61, no. 6, pp. 1684–1691, June 2012. [4.12] A. Thamrongmas and C. Charoenlarpnopparut, “Modified pole re-position technique for optimal IIR multiple notch filter design,” ECTI Trans. Electr. Eng. Electron. Commun., vol. 9, no. 1, pp. 7–15, 2011. [4.13] G. J. Dolecek and M. Laddomada, “A novel two stage nonrecursive architecture for the design of generalized comb filters,” Digital Signal Process., vol. 22, pp. 859–868, Sept. 2012. Chapter 5 [5.1] S.-C. Pei and C.-C. Tseng, “Two dimensional IIR digital notch filter design,” IEEE Trans. Circuits Syst. II, vol. 41, no. 3, pp. 227-231, Mar. 1994. [5.2] S.-C. Pei, W.-S. Lu and C.-C. Tseng, “Two-dimensional FIR notch filter design using singular value decomposition,” IEEE Trans. Circuits Syst. I, vol. 45, no. 3, pp. 290-294, Mar. 1998. [5.3] P. A. Regalia, S. K. Mitra and P. P. Vaidyanathan, “The digital all-pass filter: a versatile signal processing building block,” Proc. IEEE, vol. 76, no. 1, pp. 19-37, Jan. 1988. [5.4] P. A. Thompson, “A constrained recursive adaptive filter for enhancement of narrow-band signals in white noise,” Ph.D. dissertation, Dept. Elect. Eng., Stanford Univ., CA, Feb. 1979. [5.5] S. Y. Kung and D. V. Bhaskar Rao, “An unbiased adaptive method for retrieval of sinusoidal signals in colored noise,” in 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, San Diego, 1981, pp. 801-807. [5.6] A. Nehorai, “A minimal parameter adaptive notch filter with constrained poles and zeros,” IEEE Trans. Acoust., Speech, Signal Process., vol. 33, no. 4, pp. 983-996, Aug. 1985. [5.7] T. S. Ng, “Some aspects of an adaptive digital notch filter with constrained poles and zeros,” IEEE Trans. Acoust., Speech, Signal Process., vol. 35, no. 2, pp. 158-161, Feb. 1987. [5.8] S.-C. Pei and C.-C. Tseng, “IIR multiple notch filter design based on allpass filter”, IEEE Trans. Circuits Syst. II, vol. 44, no. 2, pp. 133-136, Feb. 1997. [5.9] R. Sameni, “A linear Kalman Notch Filter for Power-Line Interference Cancellation,” in 16th CSI International Symposium on Artificial Intelligence and Signal Processing, Shiraz, 2012, pp. 604-610. [5.10] F. J. Harris, “Transforming Half-band to Arbitrary Bandwidth” in Multirate Signal Processing For Communication Systems, 1st ed., Prentice Hall PTR Upper Saddle River, NJ, USA, 2004, pp. 290-300. [5.11] C.-L. Wu, “Adaptive Digital Allpass Based Notch Filters,” Master Thesis, National Taiwan University, 2002. [5.12] S.-C. Pei, W.-S. Lu and C.-C. Tseng, “Analytical two dimensional IIR notch filter design using outer product expansion,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 44, no. 9, pp. 765-768, Sept. 1997. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/19997 | - |
| dc.description.abstract | 訊號處理在現實生活中有很多的應用，而傳統數位訊號處理的理論可以說是相當完備。然而，隨著人類的進展，資料量的需求越來越大和複雜，傳統數位訊號處理的理論已不適合處理如此龐大且複雜的資料。
近幾年，很多的學者投入研究圖形上的訊號處理。圖形可以是一個不規則且複雜的架構。有別於以往處理的對象都是規則或是歐幾里得空間可以描述的形狀，圖形上的訊號處理的理論則可以被廣泛地應用並解決現今所遭遇的困難，像是如何對龐大的社交網絡的數據進行壓縮與還原。當然，傳統數位訊號處理的理論可以視為圖形上訊號處理理論的一種特例。 在本篇論文的第一部分，我們會先介紹圖形上的基本概念，像是圖形的傅利葉轉換、圖形的旋積、圖形相關的運算子等。接著，專注在討論對圖形的下採樣與還原，並提出一多通道架構來實現對圖形的下採樣與還原。接著與現今的方法做比較，可以發現我們的方法不但能達到完美還原圖形訊號，還能保持下採樣後圖形與原圖形的相似性。亦即，下採樣後的訊號頻譜與原訊號頻譜幾乎一致。 在論文的第二部分，我們專注在凹口濾波器的設計、分析以及如何提升凹口濾波器的效能。採用一個只需一個參數的回授架構，藉由調大該參數便能使各種類形凹口濾波器的效能提升，並用數學證明其合理性。 第一部分和第二部分看似兩個不相干的領域，一個建構在新興的圖形處理上；另一個則是建構在傳統訊號處理上。巧妙地藉由變數的轉換可以讓這兩個領域結合。因此，任何傳統濾波器皆可透過這個方法得到一個圖形上的濾波器。 | zh_TW |
| dc.description.abstract | Signal processing plays a critical role in many applications such as denoising and communication. It has really wide usages. Classical signal processing has been developed many decades and is a mature and complete field equipping with a lot of useful theories such as the sampling theory and the uncertainty principle. However, as human progress, the demand for data to describe a thing or a situation becomes larger and more complex. The classical DSP is not applicable to such complex and enormous data any more. Hence, some ideas and methods are developed.
In recent years, many researchers devote themselves to developing theories for signal processing on graphs. A graph can be an irregular and complex structure. Differently from the classical signal processing that can only deal with regular structures, the developing theories of signal processing on graphs can be widely utilized and solve difficult problems such as how to compress big data of social network and reconstruct the compressed data back as well as traffic congestion problems. Obviously, the classical DSP is a special case of the emerging graph signal processing (GSP). In the part one of this thesis, we first introduce basic concepts of signal processing on graphs such as graph Fourier transform, graph convolution and graph-related operators. Next, we will focus on downsampling as well as on reconstructing a graph signal, and then propose an M-channel to decompose a graph signal and then achieve perfect recovery. To demonstrate the effectiveness of our proposed method, the existing method based on sampling theory is compared with ours. It is easy to find that our proposed method can not only perfectly reconstruct graph signals, but also obtain a coarsened graph signal with spectral invariance and a coarsened graph with topological similarity. That is, a coarsened graph signal is strongly related to an original graph signal. In the part two of this thesis, we concentrate on the notch filter design, analysis and how to improve its performance. A feedback structure is applied to better the performance of any kinds of notch filters. The structure requires only one parameter to adjust filter performance in the frequency domain. Besides, mathematical proof and pole-zero plot are presented to demonstrate the effectiveness of the feedback structure. The part one and the part two are seemingly unrelated. One is based on the emerging field of signal processing on graph, while the other is established on the classical signal processing. We use a method to combine this two fields. Therefore, any kind of traditional filters can be transformed into a corresponding graph filter via the method. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T02:38:34Z (GMT). No. of bitstreams: 1 ntu-105-R03942061-1.pdf: 7170330 bytes, checksum: fde10706edc01c4fd5e6ff8365508a24 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 口試委員會審定書 #
誌謝 i 中文摘要 ii ABSTRACT iii CONTENTS v LIST OF FIGURES viii LIST OF TABLES xiii Chapter 1 Introduction 1 Chapter 2 From Discrete-Time Signal Processing to the Emerging Field of Signal Processing on Graphs 4 2.1 Introduction 4 2.2 Preliminaries 5 2.2.1 Discrete-Time Signals 5 2.2.2 Linear Time-Invariant Systems 6 2.2.3 Graphs and Signals on Graphs 8 2.2.4 Weighted Graphs 9 2.2.5 The Graph Laplacian 12 2.3 Transforms 13 2.3.1 The Fourier Transform and the Discrete Fourier Transform 13 2.3.2 The Graph Fourier Transform 14 2.3.3 Influence of the Underlying Graph 16 2.3.4 Bandlimited Graph Signals 18 2.4 Convolution Operators 19 2.4.1 Linear Convolution and Circular Convolution 19 2.4.2 Graph Convolution 20 2.5 Translation Operators 21 2.5.1 Traditional Translation 21 2.5.2 Graph Translation 22 2.5.3 Exponential-function-based Graph Translation 24 2.5.4 Reduced-adjacency-matrix-based Graph Translation 26 2.6 Filtering Operators 27 2.6.1 Traditional Filtering 27 2.6.2 Graph Filtering 28 2.7 Conclusion 31 Chapter 3 Perfect Recovery of Coarsened Graph Signals 47 3.1 Introduction 47 3.2 Preliminaries 48 3.3 Graph Coarsening 51 3.4 The Proposed Method: M-Channel Recovery 54 3.5 The Existing Recovering Method Based on Sampling Theory 58 3.6 Experimental Results 63 3.7 Conclusion 68 Chapter 4 Notch Filters from a Mathematical Point of View 73 4.1 Introduction 73 4.2 Mathematical Proofs 73 4.2.1 A Simple Notch Filter 73 4.2.2 Using the Feedback Structure 74 4.2.3 The Influence of the Feedback Structure 77 4.2.4 The Pole Analysis of Notch Filters 79 4.2.5 The Disadvantage and the Future Work 81 4.3 Conclusions 81 Chapter 5 All-pass-based Notch Filter Design 82 5.1 Introduction 82 5.2 The All-pass-based Notch Filter 82 5.2.1 The Mathematical Derivation 82 5.2.2 The Transformation-based Concept 87 5.2.3 The Pole-zero Relationship from a Mathematical point of view 89 5.2.4 The Pole-zero Assignment 91 5.2.5 Experimental Results 94 5.2.6 More details about the All-pass-based Notch Filter 97 5.3 Conclusions 99 REFERENCE 104 | |
| dc.language.iso | en | |
| dc.title | 圖形上的訊號處理與凹口濾波器設計 | zh_TW |
| dc.title | Signal Processing on Graphs and Notch Filter Design | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 祁忠勇,李枝宏,馮世邁 | |
| dc.subject.keyword | 圖,訊號處理,下取樣,粗化,完美還原,凹口濾波器, | zh_TW |
| dc.subject.keyword | Graphs,Signal Processing,Downsampling,Coarsening,Perfect Recovery,Notch Filter, | en |
| dc.relation.page | 113 | |
| dc.identifier.doi | 10.6342/NTU201801605 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2018-07-17 | |
| 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 |
| Appears in Collections: | 電信工程學研究所 | |
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| ntu-105-1.pdf Restricted Access | 7 MB | Adobe PDF |
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