| ISBN |
9783642818974 |
| 기타 표준번호 |
10.1007/978-3-642-81897-4 |
| 청구기호 |
QA297-299.4 |
| 형태사항 |
XII, 276p. 38 illus. online resource.
|
| 언어 |
English |
| 내용 |
1 Introduction -- 1.1 Introductory Remarks -- 1.2 Notations -- 1.3 The Structure of the Book -- 2 Elements of Number Theory and Polynomial Algebra -- 2.1 Elementary Number Theory -- 2.2 Polynomial Algebra -- 3 Fast Convolution Algorithms -- 3.1 Digital Filtering Using Cyclic Convolutions -- 3.2 Computation of Short Convolutions and Polynomial Products -- 3.3 Computation of Large Convolutions by Nesting of Small Convolutions -- 3.4 Digital Filtering by Multidimensional Techniques -- 3.5 Computation of Convolutions by Recursive Nesting of Polynomials -- 3.6 Distributed Arithmetic -- 3.7 Short Convolution and Polynomial Product Algorithms -- 4 The Fast Fourier Transform -- 4.1 The Discrete Fourier Transform -- 4.2 The Fast Fourier Transform Algorithm -- 4.3 The Rader-Brenner FFT -- 4.4 Multidimensional FFTs -- 4.5 The Bruun Algorithm -- 4.6 FFT Computation of Convolutions -- 5 Linear Filtering Computation of Discrete Fourier Transforms -- 5.1 The Chirp z-Transform Algorithm -- 5.2 Rader?�s Algorithm -- 5.3 The Prime Factor FFT -- 5.4 The Winograd Fourier Transform Algorithm (WFTA) -- 5.5 Short DFT Algorithms -- 6 Polynomial Transforms -- 6.1 Introduction to Polynomial Transforms -- 6.2 General Definition of Polynomial Transforms -- 6.3 Computation of Polynomial Transforms and Reductions -- 6.4 Two-Dimensional Filtering Using Polynomial Transforms -- 6.5 Polynomial Transforms Defined in Modified Rings -- 6.6 Complex Convolutions -- 6.7 Multidimensional Polynomial Transforms -- 7 Computation of Discrete Fourier Transforms by Polynomial Transforms -- 7.1 Computation of Multidimensional DFTs by Polynomial Transforms -- 7.2 DFTs Evaluated by Multidimensional Correlations and Polynomial Transforms -- 7.3 Comparison with the Conventional FFT -- 7.4 Odd DFT Algorithms -- 8 Number Theoretic Transforms -- 8.1 Definition of the Number Theoretic Transforms -- 8.2 Mersenne Transforms -- 8.3 Fermat Number Transforms -- 8.4 Word Length and Transform Length Limitations -- 8.5 Pseudo Transforms -- 8.6 Complex NTTs -- 8.7 Comparison with the FFT -- Appendix A Relationship Between DFT and Conyolution Polynomial Transform Algorithms -- A.1 Computation of Multidimensional DFT?�s by the Inverse Polynomial Transform Algorithm -- A.1.1 The Inverse Polynomial Transform Algorithm -- A.1.2 Complex Polynomial Transform Algorithms -- A.1.3 Round-off Error Analysis -- A.2 Computation of Multidimensional Convolutions by a Combination of the Direct and Inverse Polynomial Transform Methods -- A.2.1 Computation of Convolutions by DFT Polynomial Transform Algorithms -- A.2.2 Convolution Algorithms Based on Polynomial Transforms and Permutations -- A.3 Computation of Multidimensional Discrete Cosine Transforms by Polynomial Transforms -- A.3.1 Computation of Direct Multidimensional DCT?�s -- A.3.2 Computation of Inverse Multidimensional DCT?�s -- Appendix B Short Polynomial Product Algorithms -- Problems -- References.
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| 주제 |
Mathematics.
Numerical analysis.
Mathematics.
Numerical Analysis.
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| 보유판 및 특별호 저록 |
Springer eBooks
Printed edition: 9783540118251
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| QR CODE |
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