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.

Haitham Hassanieh, University of Illinois at Urbana Champaign
Haitham Hassanieh is an assistant professor in the Electrical and Computer Engineering and Computer Science departments at the University of Illinois at Urbana Champaign. He received his bachelor's in Computer and Communications Engineering from the American University of Beirut in 2009. He received his M.S. and Ph.D. in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology in 2011 and 2016, respectively. He works on wireless networks, sensing systems, and algorithms. He has won multiple awards including the 2017 MobiSys Best Paper Award, the 2011 SIGCOMM Best Paper Award, the Sprowls award for best thesis in computer science at MIT, the TR10 award for Technology Review Top 10 Breakthrough Technologies, and the ACM Doctoral Dissertation Award.

Table of Contents
Preface
Introduction

Part I: Theory of the Sparse Fourier Transform
Preliminaries
Simple and Practical Algorithm
Optimizing Runtime Complexity
Optimizing Sample Complexity
Numerical Evaluation

Part II: Applications of the Sparse Fourier Transform
GHz-Wide Spectrum Sensing and Decoding
Faster GPS Synchronization
Light Field Reconstruction Using Continuous Fourier Sparsity
Fast In-Vivo MRS Acquisition with Artifact Suppression
Fast Multi-Dimensional NMR Acquisition and Processing

Conclusion
Appendixes
References