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Books > Computing & IT > General theory of computing > Data structures
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The Sparse Fourier Transform (Hardcover)
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The Sparse Fourier Transform (Hardcover)
Series: ACM Books
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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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