UID:
almafu_9959327561202883
Format:
1 online resource (xxiii, 236 pages) :
,
illustrations
ISBN:
0471694630
,
9780471694632
,
9780471745433
,
047174543X
,
9780471745426
,
0471745421
,
9781601193766
,
1601193769
Content:
Discover applications of Fourier analysis on finite non-Abelian groups The majority of publications in spectral techniques consider Fourier transform on Abelian groups. However, non-Abelian groups provide notable advantages in efficient implementations of spectral methods. Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design examines aspects of Fourier analysis on finite non-Abelian groups and discusses different methods used to determine compact representations for discrete functions providing for their efficient realizations and related.
Note:
Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design; Preface; 0.1 Relationships among the chapters.; Acknowledgments; Contents; List of Figures; List of Tables; Acronyms; 1 Signals and Their Mathematical Models; 1.1 Systems; 1.2 Signals; 1.3 Mathematical Models of Signals References; References; 2 Fourier Analysis; 2.1 Representations of Groups; 2.1.1 Complete reducibility; 2.2 Fourier Transform on Finite Groups; 2.1 Group operation of S3.; 2.2 The unitary irreducible representations of S3 over C.; 2.3 The group characters of S3 over C.
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2.3 Properties of the Fourier transform2.4 The set Rw(i, j) (x) of S3 over C.; 2.5 Unitary irreducible representations of S3 over GF(11).; 2.6 The group characters of S3 over GF(11).; 2.7 The set Rw(i, j) (x) of S3 over GF(11).; 2.4 Matrix interpretation of the Fourier transform on finite non-Abelian groups; 2.5 Fast Fourier transform on finite non-Abelian groups References; 2.8 Group operation for the quaternion group Q2.; 2.9 Irreducible unitary representations of Q2 over C.; 2.1 FFT on the quaternion group Q2.; 2.2 Flow-graph for FFT algorithm for the inverse Fourier transform on Q8.
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2.10 The discrete Walsh functions wal(i, x).2.3 FFT on the dyadic group of order 8.; References; 3 Matrix Interpretation of the FFT; 3.1 Matrix interpretation of FFT on finite non-Abelian groups; 3.2 Illustrative examples; 3.1 Summary of differences between the FFT on finite Abelian and finite non-Abelian groups.; 3.2 Group operation of G2×8.; 3.3 Unitary irreducible representations of G2×8 over C.; 3.1 Structure of the flow-graph of the FFT on the group G2×8.; 3.2 Structure of the flow-graph for FFT on the group G32.
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3.3 Structure of the flow-graph for FFT on the group G32 through a part of fast Walsh transform. 3.4 Structure of the flow-graph for FFT on the group G32 using FFT on Q2.; 3.4 The unitary irreducible representations of G6×6 over GF(11).; 3.5 Structure of the flow-graph for FFT on the group G6×6.; 3.5 The group operation of G3×6.; 3.6 The unitary irreducible representations of G3×6 over C.; 3.6 Structure of the flow-graph for FFT on the group G3×6.; 3.7 Structure of the flow-graph for FFT on G24.; 3.3 Complexity of the FFT; 3.8 Structure of the flow-graph for FFT on S3.
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3.9 Structure of the flow-graph for FFT on G24 with FFT on S3.3.3.1 Complexity of calculations of the FFT; 3.10 Number of operations in FFT.; 3.7 Complexity of the FFT.; 3.8 Comparisons of domain groups.; 3.9 FFT for random functions.; 3.10 Comparison of the FFT for random functions.; 3.11 Time requirements.; 3.12 Memory requirements.; 3.3.2 Remarks on programming implementation of FFT; 3.4 FFT through decision diagrams; 3.4.1 Decision diagrams; 3.4.2 FFT on finite non-Abelian groups through DDs; 3.13 MTDD for f in Example 3.6.; 3.14 BDD for f in Example 3.7.
Additional Edition:
Print version: Stanković, Radomir S. Fourier analysis on finite groups with applications in signal processing and system design. Piscataway, NJ : IEEE Press ; Hoboken, N.J. : Wiley-Interscience, ©2005 ISBN 0471694630
Language:
English
Keywords:
Electronic books.
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Electronic books.
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Electronic books.
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Electronic books.
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/047174543X
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/047174543X
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