A Sublinear Algorithm of Sparse Fourier Transform for Nonequispaced Data

Nonequispaced Data Jing Zou 12th August 2005 Abstract We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. More precisely, we address the situation where a signal is known to consist of equispaced samples, of which only are available. This includes the case of “equispaced data with gaps”; if the ratio is smaller than 1, the available data are typically non-equispaced samples, with little or no visible trace of the equispacing of the full set of samples. We extend an approach for equispaced data that was presented in [21]; the extended algorithm reconstructs, from the incomplete data, a near-optimal -term representation with high probability , in time and space "!$#&% (') "!$#&% * + , * '.') "!$#&%/ * + 0')