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Produktbild: Multiplicative Complexity, Convolution, and the DFT

Multiplicative Complexity, Convolution, and the DFT

Aus der Reihe Signal Processing and Digital Filtering

Fr. 103.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Abbildungen

VIII, 155 pp.

Verlag

Springer

Seitenzahl

155

Maße (L/B/H)

1.5/16/24.2 cm

Gewicht

380 g

Sprache

Englisch

ISBN

978-0-387-96810-0

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Abbildungen

VIII, 155 pp.

Verlag

Springer

Seitenzahl

155

Maße (L/B/H)

1.5/16/24.2 cm

Gewicht

380 g

Sprache

Englisch

ISBN

978-0-387-96810-0

Herstelleradresse

Springer Heidelberg
Tiergartenstr. 17
69121 Heidelberg
DE
buchhandel-buch@springer.com

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  • Produktbild: Multiplicative Complexity, Convolution, and the DFT
  • 1. Introduction.- 1.1. An Overview of Multiplicative Complexity.- 1.2. Why Count Only Multiplications and Divisions?.- 1.3. Organization.- 2. Multiplicative Complexity of Linear and Bilinear Systems.- 2.1. Historical Perspective.- 2.2. Definitions and Basic Results.- 2.3. Semilinear Systems.- 2.4. Quadratic and Bilinear Systems.- 2.4.1. Properties of Quadratic Systems.- 2.4.2. Bilinear Systems and Noncommutative Algorithms.- 2.4.3. Direct Products and Direct Sums of Systems.- 2.5. Summary of Chapter 2.- 3. Convolution and Polynomial Multiplication.- 3.1. Aperiodic Convolution/Polynomial Multiplication.- 3.2. Polynomial Multiplication Modulo an Irreducible Polynomial.- 3.3. Polynomial Multiplication Modulo a General Polynomial.- 3.4. Products of a Fixed Polynomial with Several Polynomials.- 3.4.1. Equivalent Systems and Row Reduced Forms.- 3.4.2. Reduction and Inflation Mappings.- 3.4.3. Equivalence of Products with a Fixed Polynomial.- 3.4.4. Multiplicative Complexity Results.- 3.5. Products with Several Fixed Polynomials in the Same Ring.- 3.6. Products with Several Fixed Polynomials in Different Rings.- 3.7. Multivariate Polynomial Multiplication.- 3.7.1. Polynomial Products in Two Variables.- 3.7.2. Multidimensional Cyclic Convolution.- 3.8. Summary of Chapter 3.- 4. Constrained Polynomial Multiplication.- 4.1. General Input Constraints.- 4.2. Multiplication by a Symmetric Polynomial.- 4.3. Multiplication by an Antisymmetric Polynomial.- 4.4. Products of Two Symmetric Polynomials.- 4.5. Polynomial Multiplication with Restricted Outputs.- 4.5.1. Decimation of Outputs.- 4.5.2. Other Output Restrictions.- 4.6. Summary of Chapter 4.- 5. Multiplicative Complexity of Discrete Fourier Transform.- 5.1. The Discrete Fourier Transform.- 5.2. Prime Lengths.- 5.2.1. Rader's Permutation.- 5.2.2. Multiplicative Complexity.- 5.3. Powers of Prime Lengths.- 5.4. Power-of-Two Lengths.- 5.5. Arbitrary Lengths.- 5.6. DFTs with Complex-Valued Inputs.- 5.7. Multidimensional DFTs.- 5.8. Summary of Chapter 5.- 6. Restricted and Constrained DFTs.- 6.1. Restricting DFT Outputs to One Point.- 6.2. Constraining DFT Inputs to One Point.- 6.3. DFTs with Symmetric Inputs.- 6.4. Discrete Hartley Transform.- 6.5. Discrete Cosine Transform.- 6.6. Summary of Chapter 6.- Appendix A. Cyclotomic Polynomials and Their Properties.- Appendix B. Complexities of Multidimensional Cyclic Convolutions.- Appendix C. Programs for Computing Multiplicative Complexity.- Appendix D. Tabulated Complexities of the One-Dimensional DFT.- Problems.