Ideal Sequence Design in Time-Frequency Space

1. Front Matter

   Pages 1-11

   PDF

2. Introduction

   • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

   Pages 1-3

3. Review of Algebra

   • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

   Pages 1-8

4. Permutations and Permutation Matrices

   • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

   Pages 1-11

5. Finite Fourier Transform

   • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

   Pages 1-10

6. Convolution and Correlation

   • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

   Pages 1-15

7. Discrete Chirps

   • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

   Pages 1-18

8. Zak Transform

   • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

   Pages 1-17

9. Zak Space Correlation Formula

   • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

   Pages 1-7

10. Zak Space Representation of Chirps

    • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

    Pages 1-13

11. *-Permutations

    • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

    Pages 1-10

12. Permutation Sequences

    • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

    Pages 1-17

13. Modulation

    • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

    Pages 1-18

14. Sequence Sets

    • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

    Pages 1-11

15. Echo Analysis

    • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

    Pages 1-17

16. Sequence Shaping

    • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

    Pages 1-21

17. Problems

    • Myoung An, Andrzej K. Brodzik, Richard Tolimieri

    Pages 1-6

18. Back Matter

    Pages 1-7

    PDF

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?c communities with signi?cant devel- ments in harmonic analysis, ranging from abstract harmonic analysis to basic app- cations. The title of the series re?ects the importance of applications and numerical implementation, but richness and relevance of applications and implementation - pend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has ?ourished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship - tween harmonic analysis and ?elds such as signal processing, partial differential equations (PDEs), and image processing is re?ected in our state-of-the-art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

• Fourier transform
• Modulation
• Zak space
• Zak transform
• algorithms
• code
• communication
• convolution
• dielectric material
• multibeam radar and sonar imaging
• pulse radars and sonars
• sequences
• signal design
• time-frequency space
• waveform design

From the reviews:

"The book … develops a new theory leading to systematic sequence design in time-frequency space. The essential tool of this interesting method is the finite Zak transform, which provides sparse representations for the discrete Fourier transform, cyclic convolution, and correlation. Using this Zak representation, the authors construct a large class of sequence sets satisfying pairwise ideal correlation. … This interesting and well-written book will be a useful reference text for graduate students, researchers, and engineers interested in radar/sonar signal processing or communication systems." (Manfred Tasche, Zentralblatt MATH, Vol. 1160, 2009)

Policies and ethics