
- 279 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
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.
Frequently asked questions
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Information
Table of contents
- Cover
- Title Page
- Copyright
- Dedication
- Contents
- Preface
- Chapter 1 Introduction
- Part I Theory of the Sparse Fourier Transform
- Part II Applications of the Sparse Fourier Transform
- Appendix A Proofs
- Appendix B The Optimality of the Exactly k-Sparse Algorithm 4.1
- Appendix C Lower Bound of the Sparse Fourier Transform in the General Case
- Appendix D Efficient Constructions of Window Functions
- Appendix E Sample Lower Bound for the Bernoulli Distribution
- Appendix F Analysis of the QuickSync System
- Appendix G A 0.75 Million Point Sparse Fourier Transform Chip
- References
- Author Biography