A practical high-dimensional Sparse Fourier Transform

Shaogang Wang; Vishal M. Patel; Athina P. Petropulu

ICASSP 2017accepted0 citations

A practical high-dimensional Sparse Fourier Transform

Shaogang Wang, Vishal M. Patel, Athina P. Petropulu

Abstract

As compared to the FFT, the recently introduced Sparse Fourier Transform (SFT) achieves substantial reduction in the complexity of detecting frequencies in signals that are sparse in the frequency domain. However, the SFT requires the significant frequencies to be on the grid and the exact sparsity of the signal to be known. In this paper, we propose a framework that overcomes these issues. Our method makes use of a pre-permutation window to confine the leakage within finite frequency bins and the Neyman-Pearson criterion to detect weak signals without knowing the exact signal sparsity. Various numerical experiments and an application to radar target detection demonstrate the advantages of the proposed method.

BibTeX

@inproceedings{icassp2017_apracticalhighdi,
  title = {A practical high-dimensional Sparse Fourier Transform},
  author = {Shaogang Wang and Vishal M. Patel and Athina P. Petropulu},
  booktitle = {ICASSP 2017},
  year = {2017}
}