IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
A Combinatorial Aliasing-Based Sparse Fourier Transform
Pengcheng QIUFeng YU
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2015 Volume E98.A Issue 9 Pages 1968-1972

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Abstract

The sparse Fourier transform (SFT) seeks to recover k non-negligible Fourier coefficients from a k-sparse signal of length N (k«N). A single frequency signal can be recovered via the Chinese remainder theorem (CRT) with sub-sampled discrete Fourier transforms (DFTs). However, when there are multiple non-negligible coefficients, more of them may collide, and multiple stages of sub-sampled DFTs are needed to deal with such collisions. In this paper, we propose a combinatorial aliasing-based SFT (CASFT) algorithm that is robust to noise and greatly reduces the number of stages by iteratively recovering coefficients. First, CASFT detects collisions and recovers coefficients via the CRT in a single stage. These coefficients are then subtracted from each stage, and the process iterates through the other stages. With a computational complexity of O(klog klog 2N) and sample complexity of O(klog 2N), CASFT is a novel and efficient SFT algorithm.

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© 2015 The Institute of Electronics, Information and Communication Engineers
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