Author | Tolimieri, Richard. author |
---|---|
Title | Time-Frequency Representations [electronic resource] / by Richard Tolimieri, Myoung An |
Imprint | Boston, MA : Birkhรคuser Boston, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4152-2 |
Descript | XIV, 284 p. online resource |
1 Review of algebra -- 1.1 Introduction -- 1.2 Definitions and examples of groups -- 1.3 Subgroups, cosets, and quotients -- 1.4 Ideals -- 1.5 Mappings -- 1.6 Finitely generated abelian groups -- References -- 2 Linear algebra and abelian groups -- 2.1 Introduction -- 2.2 Vector space L(A) -- 3 Fourier transform over A -- 3.1 Introduction -- 3.2 Character groups -- 3.3 Character formulas -- 3.4 Duality theory -- 3.5 Character group basis -- 3.6 Fourier transform -- 3.7 Shift and multiplication operators -- References -- Problems -- 4 Poisson summation formula -- 4.1 Introduction -- 4.2 Statement and proof -- 4.3 Fourier transform of periodic functions -- 4.4 Periodization-decimation operators -- References -- Problems -- 5 Zak transform -- 5.1 Introduction -- 5.2 Fourier analysis on A x A* -- 5.3 Zak transform -- 5.4 Functional equation -- 5.5 Fourier and Zak transform -- 5.6 Isometry -- 5.7 Algorithm for computing Zak transform -- References -- Problems -- 6 Weyl-Heisenberg systems -- 6.1 Introduction -- 6.2 Translates -- 6.3 W-H systems -- 6.4 Sampling rates -- 6.5 Divide-and-conquer -- References -- Problems -- 7 Zak transform and W-H systems -- 7.1 Introduction -- 7.2 Basic results -- 7.3 Fundamental formulas -- 7.4 Zak space characterization of W-H systems -- 7.5 Zero set characterization -- Problems -- 8 Algorithms for W-H systems -- 8.1 Introduction -- 8.2 Critical sampling algorithm -- 8.3 Integer over-sampling algorithm -- 8.4 General over-sampling algorithm -- References -- Problems -- 9 Orthogonal projection theorem -- 9.1 Introduction -- 9.2 Orthogonal projection algorithm -- 9.3 Iterative W-H coefficient set algorithm -- 10 Cross-ambiguity function -- 10.1 Introduction -- 10.2 Basic results -- 10.3 Direct algorithm -- 10.4 Critical sampling algorithm -- 10.5 Integer over-sampling algorithm -- 10.6 General divide-and-conquer algorithm -- References -- Problems -- 11 Ambiguity surfaces -- 11.1 Introduction -- 11.2 Fourier transform of ambiguity surfaces -- 11.3 Formulas D1 and D2 -- References -- 12 Orthonormal W-H systems -- 12.1 Introduction -- 12.2 Orthonormal W-H systems -- References -- Problems -- 13 Duality -- 13.1 Introduction -- 13.2 Biorthogonal -- 13.3 Algorithms for computing biorthogonals -- References -- Problems -- 14 Frames -- 14.1 Introduction -- 14.2 Frame Operator -- 14.3 Frames -- 14.4 Frame biorthogonals -- 14.5 Operator interpretation -- 14.6 Tight frames -- References -- 15 Implementation -- 15.1 Introduction -- 15.2 Tensor product -- 15.3 Multidimensional arrays -- 15.4 Computing the Zak transform -- References -- Problems -- 16 Algebra of multirate structures -- 16.1 Introduction -- 16.2 Algebra -- 16.3 Exact sequences -- 16.4 Main theorem -- 16.5 Representatives mapping theorem -- 16.6 Integer matrices -- References -- Problems -- 17 Multirate structures -- 17.1 Introduction -- 17.2 Decimation operator -- 17.3 Polyphase representation -- 17.4 Integer rate bands -- 17.5 Reduction theorems -- 17.6 Decimators and expanders -- References -- 18 A Time-frequency search for stock market anomalies -- 18.1 Introduction -- 18.2 Time-frequency trees -- 18.3 Analysis of the log-differenced DJIA and S&P 500 data -- References