Improved bounds for a deterministic sublinear-time Sparse Fourier Algorithm

—This paper improves on the best-known runtime and measurement bounds for a recently proposed Deterministic sublinear-time Sparse Fourier Transform algorithm (hereafter called DSFT). In [1], [2], it is shown that DSFT can exactly reconstruct the Fourier transform (FT) of an N-bandwidth signal f, consisting of B N non-zero frequencies, using O(B2 ·polylog(N)) time and O(B2 · polylog(N)) f-samples. DSFT works by taking advantage of natural aliasing phenomena to hash a frequencysparse signal’s FT information modulo O(B·polylog(N)) pairwise coprime numbers via O(B · polylog(N)) small Discrete Fourier Transforms. Number theoretic arguments then guarantee the original DFT frequencies/coefficients can be recovered via the Chinese Remainder Theorem. DSFT’s usage of primes makes its runtime and signal sample requirements highly dependent on the sizes of sums and products of small primes. Our new bounds utilize analytic number theoretic techniques to generate improved (asymptotic) boun...

• Type: Conference
• Year: 2008
• Where: CISS
• Authors: Mark A. Iwen, Craig V. Spencer
• Keywords: CISS 2008, Fourier Transform Algorithm, Fourier Transforms, Information Management, N-bandwidth Signal F