Reconstruction of Uniformly Sampled Sequence From Nonuniformly Sampled Transient Sequence Using Symmetric Extension

In this correspondence, reconstruction of a uniformly sampled sequence from a nonuniformly sampled transient sequence using symmetric extension is described. First, a relationship between the discrete Fourier transform (DFT) of a uniformly sampled sequence and the DFT of a nonuniformly sampled sequence is obtained. From the relationship, the formula to reconstruct the DFT of a uniformly sampled sequence from the DFT of a nonuniformly sampled sequence is derived when the nonuniform sampling ratios are known. Second, a symmetric extension of the nonuniformly sampled sequence is described to avoid discontinuity that adds high-frequency content in the DFT. Finally, experimental results are presented.