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Computational and experimental group theory : AMS-ASL joint special session, interactions between logic, group theory, and computer science, January 15-16, 2003, Baltimore, Maryland / / Alexandre V. Borovik, Alexei G. Myasnikov, editors
| Computational and experimental group theory : AMS-ASL joint special session, interactions between logic, group theory, and computer science, January 15-16, 2003, Baltimore, Maryland / / Alexandre V. Borovik, Alexei G. Myasnikov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (234 p.) |
| Disciplina | 512/.21 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Permutation groups
Non-Abelian groups Quantum theory - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-8218-7939-1
0-8218-5684-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Quantum algorithms in group theory""; ""1. Introduction""; ""2. The basics of quantum computing""; ""3. The Deutsch�Jozsa algorithm""; ""4. Shor's algorithm and factoring integers""; ""5. Grover's algorithm""; ""6. Watrous' algorithms for solvable groups""; ""References""; ""Genetic algorithms and equations in free groups and semigroups""; ""1. Introduction""; ""2. A genetic algorithm framework on the free group""; ""3. Choosing problems""; ""4. Traceback""; ""5. Coevolution""; ""6. The genus problem and equations in a free semigroup""
""7. The algorithm for the genus problem""""8. Discussion""; ""9. One more case study: restricted conjugacy problem in free partially commutative groups""; ""References""; ""One variable equations in free groups via context free languages""; ""1. Introduction""; ""2. Results from Language Theory""; ""3. Proof of Theorem 1""; ""References""; ""Whitehead method and genetic algorithms""; ""1. Introduction""; ""2. Whitehead method""; ""3. Description of the genetic algorithm""; ""4. Experiments and results""; ""5. Time complexity of GWA""; ""6. Mathematical problems arising from the experiments"" ""References""""The structure of automorphic conjugacy in the free group of rank two""; ""1. The automorphism graph of F2""; ""2. Combinatorial groundwork""; ""3. The structure within levels""; ""4. Algorithmic applications""; ""5. Computational tools""; ""6. Conclusions and future work""; ""References""; ""Pattern recognition approaches to solving combinatorial problems in free groups""; ""1. Introduction""; ""2. General remarks on pattern recognition tasks""; ""3. Feature vectors""; ""4. Pattern recognition tools and models""; ""5. Recognizing Whitehead minimal words in free groups"" ""References""""Experimenting with primitive elements in F2"" |
| Record Nr. | UNINA-9910480012603321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computational and experimental group theory : AMS-ASL joint special session, interactions between logic, group theory, and computer science, January 15-16, 2003, Baltimore, Maryland / / Alexandre V. Borovik, Alexei G. Myasnikov, editors
| Computational and experimental group theory : AMS-ASL joint special session, interactions between logic, group theory, and computer science, January 15-16, 2003, Baltimore, Maryland / / Alexandre V. Borovik, Alexei G. Myasnikov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (234 p.) |
| Disciplina | 512/.21 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Permutation groups
Non-Abelian groups Quantum theory - Mathematics |
| ISBN |
0-8218-7939-1
0-8218-5684-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Quantum algorithms in group theory""; ""1. Introduction""; ""2. The basics of quantum computing""; ""3. The Deutsch�Jozsa algorithm""; ""4. Shor's algorithm and factoring integers""; ""5. Grover's algorithm""; ""6. Watrous' algorithms for solvable groups""; ""References""; ""Genetic algorithms and equations in free groups and semigroups""; ""1. Introduction""; ""2. A genetic algorithm framework on the free group""; ""3. Choosing problems""; ""4. Traceback""; ""5. Coevolution""; ""6. The genus problem and equations in a free semigroup""
""7. The algorithm for the genus problem""""8. Discussion""; ""9. One more case study: restricted conjugacy problem in free partially commutative groups""; ""References""; ""One variable equations in free groups via context free languages""; ""1. Introduction""; ""2. Results from Language Theory""; ""3. Proof of Theorem 1""; ""References""; ""Whitehead method and genetic algorithms""; ""1. Introduction""; ""2. Whitehead method""; ""3. Description of the genetic algorithm""; ""4. Experiments and results""; ""5. Time complexity of GWA""; ""6. Mathematical problems arising from the experiments"" ""References""""The structure of automorphic conjugacy in the free group of rank two""; ""1. The automorphism graph of F2""; ""2. Combinatorial groundwork""; ""3. The structure within levels""; ""4. Algorithmic applications""; ""5. Computational tools""; ""6. Conclusions and future work""; ""References""; ""Pattern recognition approaches to solving combinatorial problems in free groups""; ""1. Introduction""; ""2. General remarks on pattern recognition tasks""; ""3. Feature vectors""; ""4. Pattern recognition tools and models""; ""5. Recognizing Whitehead minimal words in free groups"" ""References""""Experimenting with primitive elements in F2"" |
| Record Nr. | UNINA-9910788667303321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computational and experimental group theory : AMS-ASL joint special session, interactions between logic, group theory, and computer science, January 15-16, 2003, Baltimore, Maryland / / Alexandre V. Borovik, Alexei G. Myasnikov, editors
| Computational and experimental group theory : AMS-ASL joint special session, interactions between logic, group theory, and computer science, January 15-16, 2003, Baltimore, Maryland / / Alexandre V. Borovik, Alexei G. Myasnikov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (234 p.) |
| Disciplina | 512/.21 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Permutation groups
Non-Abelian groups Quantum theory - Mathematics |
| ISBN |
0-8218-7939-1
0-8218-5684-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Quantum algorithms in group theory""; ""1. Introduction""; ""2. The basics of quantum computing""; ""3. The Deutsch�Jozsa algorithm""; ""4. Shor's algorithm and factoring integers""; ""5. Grover's algorithm""; ""6. Watrous' algorithms for solvable groups""; ""References""; ""Genetic algorithms and equations in free groups and semigroups""; ""1. Introduction""; ""2. A genetic algorithm framework on the free group""; ""3. Choosing problems""; ""4. Traceback""; ""5. Coevolution""; ""6. The genus problem and equations in a free semigroup""
""7. The algorithm for the genus problem""""8. Discussion""; ""9. One more case study: restricted conjugacy problem in free partially commutative groups""; ""References""; ""One variable equations in free groups via context free languages""; ""1. Introduction""; ""2. Results from Language Theory""; ""3. Proof of Theorem 1""; ""References""; ""Whitehead method and genetic algorithms""; ""1. Introduction""; ""2. Whitehead method""; ""3. Description of the genetic algorithm""; ""4. Experiments and results""; ""5. Time complexity of GWA""; ""6. Mathematical problems arising from the experiments"" ""References""""The structure of automorphic conjugacy in the free group of rank two""; ""1. The automorphism graph of F2""; ""2. Combinatorial groundwork""; ""3. The structure within levels""; ""4. Algorithmic applications""; ""5. Computational tools""; ""6. Conclusions and future work""; ""References""; ""Pattern recognition approaches to solving combinatorial problems in free groups""; ""1. Introduction""; ""2. General remarks on pattern recognition tasks""; ""3. Feature vectors""; ""4. Pattern recognition tools and models""; ""5. Recognizing Whitehead minimal words in free groups"" ""References""""Experimenting with primitive elements in F2"" |
| Record Nr. | UNINA-9910812588003321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Crossed products by Hecke pairs / / Rui Palma
| Crossed products by Hecke pairs / / Rui Palma |
| Autore | Palma Rui <1985-> |
| Pubbl/distr/stampa | Providence, RI : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (156 pages) |
| Disciplina | 512/.2 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Crossed products
Hecke algebras Group algebras Non-Abelian groups C*-algebras |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-4377-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910481036703321 |
Palma Rui <1985->
|
||
| Providence, RI : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Crossed products by Hecke pairs / / Rui Palma
| Crossed products by Hecke pairs / / Rui Palma |
| Autore | Palma Rui <1985-> |
| Pubbl/distr/stampa | Providence, RI : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (156 pages) |
| Disciplina | 512/.2 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Crossed products
Hecke algebras Group algebras Non-Abelian groups C*-algebras |
| ISBN | 1-4704-4377-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910794922303321 |
|
Palma Rui <1985->
|
||
| Providence, RI : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Crossed products by Hecke pairs / / Rui Palma
| Crossed products by Hecke pairs / / Rui Palma |
| Autore | Palma Rui <1985-> |
| Pubbl/distr/stampa | Providence, RI : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (156 pages) |
| Disciplina | 512/.2 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Crossed products
Hecke algebras Group algebras Non-Abelian groups C*-algebras |
| ISBN | 1-4704-4377-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910806847503321 |
|
Palma Rui <1985->
|
||
| Providence, RI : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankoviâc, Claudio Moraga, Jaakko Astola
| Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankoviâc, Claudio Moraga, Jaakko Astola |
| Autore | Stankoviâc Radomir S. |
| Pubbl/distr/stampa | Piscataway, New Jersey : , : IEEE Press, , c2005 |
| Descrizione fisica | 1 online resource (262 p.) |
| Disciplina |
621.3822
621.38220151 |
| Altri autori (Persone) |
MoragaClaudio
AstolaJaakko T |
| Soggetto topico |
Signal processing - Mathematics
Fourier analysis Non-Abelian groups |
| ISBN |
1-280-27793-9
9786610277933 0-471-74543-X 1-60119-376-9 0-471-74542-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface -- Acknowledgments -- Acronyms -- 1 Signals and Their Mathematical Models -- 1.1 Systems -- 1.2 Signals -- 1.3 Mathematical Models of Signals -- References -- 2 Fourier Analysis -- 2.1 Representations of Groups -- 2.1.1 Complete Reducibility -- 2.2 Fourier Transform on Finite Groups -- 2.3 Properties of the Fourier Transform -- 2.4 Matrix Interpretation of the Fourier Transform on Finite Non-Abelian Groups -- 2.5 Fast Fourier Transform on Finite Non-Abelian Groups -- References -- 3 Matrix Interpretation of the FFT -- 3.1 Matrix Interpretation of FFT on Finite Non-Abelian Groups -- 3.2 Illustrative Examples -- 3.3 Complexity of the FFT -- 3.3.1 Complexity of Calculations of the FFT -- 3.3.2 Remarks on Programming Implememtation of FFT -- 3.4 FFT Through Decision Diagrams -- 3.4.1 Decision Diagrams -- 3.4.2 FFT on Finite Non-Abelian Groups Through DDs -- 3.4.3 MMTDs for the Fourier Spectrum -- 3.4.4 Complexity of DDs Calculation Methods -- References -- 4 Optimization of Decision Diagrams -- 4.1 Reduction Possibilities in Decision Diagrams -- 4.2 Group-Theoretic Interpretation of DD -- 4.3 Fourier Decision Diagrams -- 4.3.1 Fourier Decision Trees -- 4.3.2 Fourier Decision Diagrams -- 4.4 Discussion of Different Decompositions -- 4.4.1 Algorithm for Optimization of DDs -- 4.5 Representation of Two-Variable Function Generator -- 4.6 Representation of Adders by Fourier DD -- 4.7 Representation of Multipliers by Fourier DD -- 4.8 Complexity of NADD -- 4.9 Fourier DDs with Preprocessing -- 4.9.1 Matrix-valued Functions -- 4.9.2 Fourier Transform for Matrix-Valued Functions -- 4.10 Fourier Decision Trees with Preprocessing -- 4.11 Fourier Decision Diagrams with Preprocessing -- 4.12 Construction of FNAPDD -- 4.13 Algorithm for Construction of FNAPDD -- 4.13.1 Algorithm for Representation -- 4.14 Optimization of FNAPDD -- References -- 5 Functional Expressions on Quaternion Groups -- 5.1 Fourier Expressions on Finite Dyadic Groups -- 5.1.1 Finite Dyadic Groups -- 5.2 Fourier Expressions on Q2.
5.3 Arithmetic Expressions -- 5.4 Arithmetic Expressions from Walsh Expansions -- 5.5 Arithmetic Expressions on Q2 -- 5.5.1 Arithmetic Expressions and Arithmetic-Haar Expressions -- 5.5.2 Arithmetic-Haar Expressions and Kronecker Expressions -- 5.6 Different Polarity Polynomials Expressions -- 5.6.1 Fixed-Polarity Fourier Expressions in C(Q2) -- 5.6.2 Fixed-Polarity Arithmetic-Haar |
| Record Nr. | UNISA-996212283503316 |
|
Stankoviâc Radomir S.
|
||
| Piscataway, New Jersey : , : IEEE Press, , c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankoviâc, Claudio Moraga, Jaakko Astola
| Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankoviâc, Claudio Moraga, Jaakko Astola |
| Autore | Stankoviâc Radomir S. |
| Pubbl/distr/stampa | Piscataway, New Jersey : , : IEEE Press, , c2005 |
| Descrizione fisica | 1 online resource (262 p.) |
| Disciplina |
621.3822
621.38220151 |
| Altri autori (Persone) |
MoragaClaudio
AstolaJaakko T |
| Soggetto topico |
Signal processing - Mathematics
Fourier analysis Non-Abelian groups |
| ISBN |
1-280-27793-9
9786610277933 0-471-74543-X 1-60119-376-9 0-471-74542-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface -- Acknowledgments -- Acronyms -- 1 Signals and Their Mathematical Models -- 1.1 Systems -- 1.2 Signals -- 1.3 Mathematical Models of Signals -- References -- 2 Fourier Analysis -- 2.1 Representations of Groups -- 2.1.1 Complete Reducibility -- 2.2 Fourier Transform on Finite Groups -- 2.3 Properties of the Fourier Transform -- 2.4 Matrix Interpretation of the Fourier Transform on Finite Non-Abelian Groups -- 2.5 Fast Fourier Transform on Finite Non-Abelian Groups -- References -- 3 Matrix Interpretation of the FFT -- 3.1 Matrix Interpretation of FFT on Finite Non-Abelian Groups -- 3.2 Illustrative Examples -- 3.3 Complexity of the FFT -- 3.3.1 Complexity of Calculations of the FFT -- 3.3.2 Remarks on Programming Implememtation of FFT -- 3.4 FFT Through Decision Diagrams -- 3.4.1 Decision Diagrams -- 3.4.2 FFT on Finite Non-Abelian Groups Through DDs -- 3.4.3 MMTDs for the Fourier Spectrum -- 3.4.4 Complexity of DDs Calculation Methods -- References -- 4 Optimization of Decision Diagrams -- 4.1 Reduction Possibilities in Decision Diagrams -- 4.2 Group-Theoretic Interpretation of DD -- 4.3 Fourier Decision Diagrams -- 4.3.1 Fourier Decision Trees -- 4.3.2 Fourier Decision Diagrams -- 4.4 Discussion of Different Decompositions -- 4.4.1 Algorithm for Optimization of DDs -- 4.5 Representation of Two-Variable Function Generator -- 4.6 Representation of Adders by Fourier DD -- 4.7 Representation of Multipliers by Fourier DD -- 4.8 Complexity of NADD -- 4.9 Fourier DDs with Preprocessing -- 4.9.1 Matrix-valued Functions -- 4.9.2 Fourier Transform for Matrix-Valued Functions -- 4.10 Fourier Decision Trees with Preprocessing -- 4.11 Fourier Decision Diagrams with Preprocessing -- 4.12 Construction of FNAPDD -- 4.13 Algorithm for Construction of FNAPDD -- 4.13.1 Algorithm for Representation -- 4.14 Optimization of FNAPDD -- References -- 5 Functional Expressions on Quaternion Groups -- 5.1 Fourier Expressions on Finite Dyadic Groups -- 5.1.1 Finite Dyadic Groups -- 5.2 Fourier Expressions on Q2.
5.3 Arithmetic Expressions -- 5.4 Arithmetic Expressions from Walsh Expansions -- 5.5 Arithmetic Expressions on Q2 -- 5.5.1 Arithmetic Expressions and Arithmetic-Haar Expressions -- 5.5.2 Arithmetic-Haar Expressions and Kronecker Expressions -- 5.6 Different Polarity Polynomials Expressions -- 5.6.1 Fixed-Polarity Fourier Expressions in C(Q2) -- 5.6.2 Fixed-Polarity Arithmetic-Haar |
| Record Nr. | UNINA-9910143559003321 |
|
Stankoviâc Radomir S.
|
||
| Piscataway, New Jersey : , : IEEE Press, , c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankoviâc, Claudio Moraga, Jaakko Astola
| Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankoviâc, Claudio Moraga, Jaakko Astola |
| Autore | Stankoviâc Radomir S. |
| Pubbl/distr/stampa | Piscataway, New Jersey : , : IEEE Press, , c2005 |
| Descrizione fisica | 1 online resource (262 p.) |
| Disciplina |
621.3822
621.38220151 |
| Altri autori (Persone) |
MoragaClaudio
AstolaJaakko T |
| Soggetto topico |
Signal processing - Mathematics
Fourier analysis Non-Abelian groups |
| ISBN |
1-280-27793-9
9786610277933 0-471-74543-X 1-60119-376-9 0-471-74542-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface -- Acknowledgments -- Acronyms -- 1 Signals and Their Mathematical Models -- 1.1 Systems -- 1.2 Signals -- 1.3 Mathematical Models of Signals -- References -- 2 Fourier Analysis -- 2.1 Representations of Groups -- 2.1.1 Complete Reducibility -- 2.2 Fourier Transform on Finite Groups -- 2.3 Properties of the Fourier Transform -- 2.4 Matrix Interpretation of the Fourier Transform on Finite Non-Abelian Groups -- 2.5 Fast Fourier Transform on Finite Non-Abelian Groups -- References -- 3 Matrix Interpretation of the FFT -- 3.1 Matrix Interpretation of FFT on Finite Non-Abelian Groups -- 3.2 Illustrative Examples -- 3.3 Complexity of the FFT -- 3.3.1 Complexity of Calculations of the FFT -- 3.3.2 Remarks on Programming Implememtation of FFT -- 3.4 FFT Through Decision Diagrams -- 3.4.1 Decision Diagrams -- 3.4.2 FFT on Finite Non-Abelian Groups Through DDs -- 3.4.3 MMTDs for the Fourier Spectrum -- 3.4.4 Complexity of DDs Calculation Methods -- References -- 4 Optimization of Decision Diagrams -- 4.1 Reduction Possibilities in Decision Diagrams -- 4.2 Group-Theoretic Interpretation of DD -- 4.3 Fourier Decision Diagrams -- 4.3.1 Fourier Decision Trees -- 4.3.2 Fourier Decision Diagrams -- 4.4 Discussion of Different Decompositions -- 4.4.1 Algorithm for Optimization of DDs -- 4.5 Representation of Two-Variable Function Generator -- 4.6 Representation of Adders by Fourier DD -- 4.7 Representation of Multipliers by Fourier DD -- 4.8 Complexity of NADD -- 4.9 Fourier DDs with Preprocessing -- 4.9.1 Matrix-valued Functions -- 4.9.2 Fourier Transform for Matrix-Valued Functions -- 4.10 Fourier Decision Trees with Preprocessing -- 4.11 Fourier Decision Diagrams with Preprocessing -- 4.12 Construction of FNAPDD -- 4.13 Algorithm for Construction of FNAPDD -- 4.13.1 Algorithm for Representation -- 4.14 Optimization of FNAPDD -- References -- 5 Functional Expressions on Quaternion Groups -- 5.1 Fourier Expressions on Finite Dyadic Groups -- 5.1.1 Finite Dyadic Groups -- 5.2 Fourier Expressions on Q2.
5.3 Arithmetic Expressions -- 5.4 Arithmetic Expressions from Walsh Expansions -- 5.5 Arithmetic Expressions on Q2 -- 5.5.1 Arithmetic Expressions and Arithmetic-Haar Expressions -- 5.5.2 Arithmetic-Haar Expressions and Kronecker Expressions -- 5.6 Different Polarity Polynomials Expressions -- 5.6.1 Fixed-Polarity Fourier Expressions in C(Q2) -- 5.6.2 Fixed-Polarity Arithmetic-Haar |
| Record Nr. | UNINA-9910829976203321 |
|
Stankoviâc Radomir S.
|
||
| Piscataway, New Jersey : , : IEEE Press, , c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankovic, Claudio Moraga, Jaakko Astola
| Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankovic, Claudio Moraga, Jaakko Astola |
| Autore | Stankovic Radomir S |
| Pubbl/distr/stampa | Piscataway, NJ, : IEEE Press |
| Descrizione fisica | 1 online resource (262 p.) |
| Disciplina | 621.382/2 |
| Altri autori (Persone) |
MoragaClaudio
AstolaJaakko |
| Soggetto topico |
Signal processing - Mathematics
Fourier analysis Non-Abelian groups |
| ISBN |
1-280-27793-9
9786610277933 0-471-74543-X 1-60119-376-9 0-471-74542-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface -- Acknowledgments -- Acronyms -- 1 Signals and Their Mathematical Models -- 1.1 Systems -- 1.2 Signals -- 1.3 Mathematical Models of Signals -- References -- 2 Fourier Analysis -- 2.1 Representations of Groups -- 2.1.1 Complete Reducibility -- 2.2 Fourier Transform on Finite Groups -- 2.3 Properties of the Fourier Transform -- 2.4 Matrix Interpretation of the Fourier Transform on Finite Non-Abelian Groups -- 2.5 Fast Fourier Transform on Finite Non-Abelian Groups -- References -- 3 Matrix Interpretation of the FFT -- 3.1 Matrix Interpretation of FFT on Finite Non-Abelian Groups -- 3.2 Illustrative Examples -- 3.3 Complexity of the FFT -- 3.3.1 Complexity of Calculations of the FFT -- 3.3.2 Remarks on Programming Implememtation of FFT -- 3.4 FFT Through Decision Diagrams -- 3.4.1 Decision Diagrams -- 3.4.2 FFT on Finite Non-Abelian Groups Through DDs -- 3.4.3 MMTDs for the Fourier Spectrum -- 3.4.4 Complexity of DDs Calculation Methods -- References -- 4 Optimization of Decision Diagrams -- 4.1 Reduction Possibilities in Decision Diagrams -- 4.2 Group-Theoretic Interpretation of DD -- 4.3 Fourier Decision Diagrams -- 4.3.1 Fourier Decision Trees -- 4.3.2 Fourier Decision Diagrams -- 4.4 Discussion of Different Decompositions -- 4.4.1 Algorithm for Optimization of DDs -- 4.5 Representation of Two-Variable Function Generator -- 4.6 Representation of Adders by Fourier DD -- 4.7 Representation of Multipliers by Fourier DD -- 4.8 Complexity of NADD -- 4.9 Fourier DDs with Preprocessing -- 4.9.1 Matrix-valued Functions -- 4.9.2 Fourier Transform for Matrix-Valued Functions -- 4.10 Fourier Decision Trees with Preprocessing -- 4.11 Fourier Decision Diagrams with Preprocessing -- 4.12 Construction of FNAPDD -- 4.13 Algorithm for Construction of FNAPDD -- 4.13.1 Algorithm for Representation -- 4.14 Optimization of FNAPDD -- References -- 5 Functional Expressions on Quaternion Groups -- 5.1 Fourier Expressions on Finite Dyadic Groups -- 5.1.1 Finite Dyadic Groups -- 5.2 Fourier Expressions on Q2.
5.3 Arithmetic Expressions -- 5.4 Arithmetic Expressions from Walsh Expansions -- 5.5 Arithmetic Expressions on Q2 -- 5.5.1 Arithmetic Expressions and Arithmetic-Haar Expressions -- 5.5.2 Arithmetic-Haar Expressions and Kronecker Expressions -- 5.6 Different Polarity Polynomials Expressions -- 5.6.1 Fixed-Polarity Fourier Expressions in C(Q2) -- 5.6.2 Fixed-Polarity Arithmetic-Haar |
| Record Nr. | UNINA-9910876824603321 |
|
Stankovic Radomir S
|
||
| Piscataway, NJ, : IEEE Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
