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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Symmetries and Groups in Signal Processing: An Introduction

Symmetries and Groups in Signal Processing: An Introduction

Sinha, Virendra P.

Paperback

Series: Signals and Communication Technology

Technology & EngineeringGeneral Computers

ISBN10: 9400733003
ISBN13: 9789400733008
Publisher: Springer
Published: Oct 13 2012
Pages: 160
Weight: 0.56
Height: 0.37 Width: 6.14 Depth: 9.21
Language: English
Preface. 1 Signals and Signal Spaces: A Structural Viewpoint. 1.1 What is a Signal? 1.2 Spaces and Structures. 1.3 Signal Spaces and Systems. 1.4 Linearity, Shift-Invariance and Causality. 1.5 Convolutional Algebra and the Z-Transform. 1.6 Shifts, Transforms and Spectra. 2 Algebraic Preliminaries. 2.1 What's in a Definition? 2.2 Set Theoretic Notation. 2.3 Relations and Operations. 2.4 Groups. 2.5 Vector Spaces. 2.6 Posets, Lattices, and Boolean Algebras. 2.7 Closing Remarks. 3 Measurement, Modeling, and Metaphors. 3.1 Archimedes and the Tortoise. 3.2 The Representational Approach. 3.3 Metaphors. 4 Symmetries, Automorphisms and Groups. 4.1 Introduction. 4.2 Symmetries and Automorphisms. 4.3 Groups of Automorphisms. 4.4 Symmetries of Linear Transformations. 4.5 Symmetry Based Decompositions. 5 Representations of Finite Groups. 5.1 The Notion of Representation. 5.2 Matrix Representations of Groups. 5.3 Automorphisms of a Vector Space. 5.4 Group Representations in GL(V). 5.5 Reducible and Irreducible Representations. 5.6 Reducibility of Representations. 5.7 Schur's Lemma and the Orthogonality Theorem. 5.8 Characters and Their Properties. 5.9 Constructing Irreducible Representations. 5.10 Complete Reduction of Representations. 5.11FurtheronReduction. 6 Signal Processing and Representation Theory. 6.1 Signals as Functions on Groups. 6.2 Symmetries of Linear Equations. 6.3 Fast Discrete Signal Transforms. A Parentheses, Their Proper Pairing, and Associativity. A.1 Proper Pairing of Parentheses. A.2 Parenthese and the Associative Law. Index.

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