Transforms and Fast Algorithms for Signal Analysis and Representations / by Guoan Bi, Yonghong Zeng
(Applied and Numerical Harmonic Analysis)
| データ種別 | 電子ブック |
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| 出版情報 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser , 2004 |
| 本文言語 | 英語 |
| 大きさ | XIX, 422 p : online resource |
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| 内容注記 | 1 Introduction 1.1 Discrete linear transforms 1.2 Fast algorithms 1.3 New transforms 1.4 Organization of the book References 2 Polynomial Transforms and Their Fast Algorithms 2.1 Basic number theory 2.2 Basic polynomial theory 2.3 1D polynomial transform 2.4 Fast polynomial transform 2.5 MD polynomial transform and fast algorithm 2.6 Chapter summary References 3 Fast Fourier Transform Algorithms 3.1 Introduction 3.2 Radix-2 and split-radix algorithms 3.3 Generalized split-radix algorithm 3.4 Prime factor algorithms 3.5 Generalized 2D split-radix algorithms 3.6 Fast algorithms for generalized DFT 3.7 Polynomial transform algorithms for MD DFT 3.8 Chapter summary 4 Fast Algorithms for 1D Discrete Hartley Transform 4.1 Introduction 4.2 Split-radix algorithms 4.3 Generalized split-radix algorithms 4.4 Radix-2 algorithms for type-II, -III and -IV DHTs 4.5 Prime factor algorithms 4.6 Radix-q algorithms 4.7 Fast algorithms using type-I DHT 4.8 Chapter summary 5 Fast Algorithms for MD Discrete Hartley Transform 5.1 Introduction 5.2 Split-radix algorithms for 2D type-I DHT 5.3 Fast algorithms for 2D type-II, -III and -IV DHTs 5.4 Fast algorithms based on type-I DHT 5.5 PT-based radix-2 algorithm for MD type-I DHT 5.6 PT-based radix-2 algorithm for MD type-II DHT 5.7 PT-based radix-q algorithm for MD type-I DHT 5.8 PT-based radix-q algorithm for MD type-II DHT 5.9 Chapter summary References 6 Fast Algorithms for 1D Discrete Cosine Transform 6.1 Introduction 6.2 Radix-2 algorithms 6.3 Prime factor algorithms 6.4 Radix-q algorithms 6.5 Fast algorithms based on type-I bCT 6.6 Chapter summary 7 Fast Algorithms for MD Discrete Cosine Transform 7.1 Introduction 7.2 Algorithms for 2D type-I, -II and -III DCTs 7.3 Prime factor algorithm for MD DCT 7.4 PT-based radix-2 algorithm for MD type-II DCT 7.5 PT-based radix-2 algorithm for MD type-III DCT 7.6 PT-based radix-q algorithm for MD type-II DCT 7.7 PT-based radix-q algorithm for MD type-III DCT 7.8 Chapter summary 8 Integer Transforms and Fast Algorithms 8.1 Introduction 8.2 Preliminaries 8.3 Integer DCT and fast algorithms 8.4 Integer DHT and fast algorithms 8.5 MD Integer DCT and fast algorithms 8.6 MD Integer DHT and fast algorithms 8.7 Chapter summary References 9 New Methods of Time-Frequency Analysis 9.1 Introduction 9.2 Preliminaries 9.3 Harmonic transform 9.4 Tomographic time-frequency transform 9.5 Chapter summary References |
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| 一般注記 | . . . that is what learning is. You suddenly understand something you've un derstood all your life, but in a new way. Various transforms have been widely used in diverse applications of science, engineering and technology. New transforms are emerging to solve many problems, which may have been left unsolved in the past, or newly created by modern science or technologies. Various meth ods have been continuously reported to improve the implementation of these transforms. Early developments of fast algorithms for discrete transforms have significantly stimulated the advance of digital signal processing technologies. More than 40 years after fast Fourier transform algorithms became known, several discrete transforms, including the discrete Hart ley transform and discrete cosine transform, were proposed and widely used for numerous applications. Although they all are related to the discrete Fourier transform, different fast algorithms and their implementations have to be separately developed to minimize compu tational complexity and implementation costs. In spite of the tremendous increase in the speed of computers or processors, the demands for higher processing throughout seemingly never ends. Fast algorithms have become more important than ever for modern applications to become a reality. Many new algorithms recently reported in the literature have led to important improvements upon a number of issues, which will be addressed in this book. Some discrete transforms are not suitable for signals that have time-varying frequency components. Although several approaches are available for such applications, various inher ent problems still remain unsolved |
| 著者標目 | *Bi, Guoan author Zeng, Yonghong author SpringerLink (Online service) |
| 件 名 | LCSH:Engineering LCSH:Algorithms LCSH:Fourier analysis LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Electrical engineering FREE:Engineering FREE:Communications Engineering, Networks FREE:Appl.Mathematics/Computational Methods of Engineering FREE:Applications of Mathematics FREE:Algorithm Analysis and Problem Complexity FREE:Fourier Analysis FREE:Algorithms |
| 分 類 | DC23:621.382 |
| 巻冊次 | ISBN:9780817682200 
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| ISBN | 9780817682200 |
| URL | http://dx.doi.org/10.1007/978-0-8176-8220-0 |
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