The Sparse Fourier Transform
eBook - ePub

The Sparse Fourier Transform

  1. 279 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

The Sparse Fourier Transform

About this book

The Fourier transform is one of the most fundamental tools for computing the frequency representation of signals. It plays a central role in signal processing, communications, audio and video compression, medical imaging, genomics, astronomy, as well as many other areas. Because of its widespread use, fast algorithms for computing the Fourier transform can benefit a large number of applications. The fastest algorithm for computing the Fourier transform is the Fast Fourier Transform (FFT), which runs in near-linear time making it an indispensable tool for many applications. However, today, the runtime of the FFT algorithm is no longer fast enough especially for big data problems where each dataset can be few terabytes. Hence, faster algorithms that run in sublinear time, i.e., do not even sample all the data points, have become necessary.

This book addresses the above problem by developing the Sparse Fourier Transform algorithms and building practical systems that use these algorithms to solve key problems in six different applications: wireless networks; mobile systems; computer graphics; medical imaging; biochemistry; and digital circuits.

This is a revised version of the thesis that won the 2016 ACM Doctoral Dissertation Award.

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Yes, you can access The Sparse Fourier Transform by Haitham Hassanieh in PDF and/or ePUB format, as well as other popular books in Computer Science & Computer Science General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. Chapter 1 Introduction
  8. Part I Theory of the Sparse Fourier Transform
  9. Part II Applications of the Sparse Fourier Transform
  10. Appendix A Proofs
  11. Appendix B The Optimality of the Exactly k-Sparse Algorithm 4.1
  12. Appendix C Lower Bound of the Sparse Fourier Transform in the General Case
  13. Appendix D Efficient Constructions of Window Functions
  14. Appendix E Sample Lower Bound for the Bernoulli Distribution
  15. Appendix F Analysis of the QuickSync System
  16. Appendix G A 0.75 Million Point Sparse Fourier Transform Chip
  17. References
  18. Author Biography