Название: The Sparse Fourier Transform Автор: Haitham Hassanieh
Издательство: ACM Books
Год: 2018
Страниц: 280
Язык: английский
Формат: pdf (true)
Размер: 53.3 MB
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.
Part I of the book focuses on the theory front. It introduces the Sparse Fourier Transform algorithms: a family of sublinear time algorithms for computing the Fourier transform faster than FFT. The Sparse Fourier Transform is based on the insight that many real-world signals are sparse, i.e., most of the frequencies have negligible contribution to the overall signal. Exploiting this sparsity, the book introduces several new algorithms which encompass two main axes:
1) Runtime Complexity
2) Sampling Complexity
Part II of the book focuses on the systems front. It develops software and hardware architectures for leveraging the Sparse Fourier Transform to address practical problems in applied fields. The systems customize the theoretical algorithms to capture the structure of sparsity in each application, and hence maximize the resulting gains. All systems are prototyped and evaluated in accordance with the standards of each application domain. The following list gives an overview of the systems presented in this book:
- Wireless Networks
- Mobile Systems
- Computer Graphics
- Medical Imaging
- Biochemistry
- Digital Circuits
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.
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