Recovery of Integer Signals from Limited DFT Samples: Lattice Methods and Stability Analysis
Abstract
We analyze lattice-based algorithms for recovering integer-valued signals from partial discrete Fourier transform (DFT) measurements. These algorithms formulate signal recovery as the problem of finding short vectors in an appropriately constructed lattice. We derive parameter estimates that predict the regimes required for successful recovery and quantify how these estimates depend on the signal length, the error of an initial guess, and the number of sampled DFT coefficients. The analysis also reveals a close connection between the lattice parameters and the precision of the measured DFT coefficients, providing insight into the numerical stability of the inversion. Numerical experiments demonstrate close agreement between the theoretical predictions and observed recovery thresholds over a broad range of problem parameters.
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BibTeX
@misc{levinson2026recovery,
title = {{Recovery of Integer Signals from Limited DFT Samples: Lattice Methods and Stability Analysis}},
author = {Howard Levinson and Isaac Viviano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.17024},
eprint = {2608.17024},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17024},
}
RIS
TY - UNPB
TI - Recovery of Integer Signals from Limited DFT Samples: Lattice Methods and Stability Analysis
AU - Howard Levinson
AU - Isaac Viviano
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2608.17024
UR - https://arxiv.org/abs/2608.17024
AB - We analyze lattice-based algorithms for recovering integer-valued signals from partial discrete Fourier transform (DFT) measurements. These algorithms formulate signal recovery as the problem of finding short vectors in an appropriately constructed lattice. We derive parameter estimates that predict the regimes required for successful recovery and quantify how these estimates depend on the signal length, the error of an initial guess, and the number of sampled DFT coefficients. The analysis also reveals a close connection between the lattice parameters and the precision of the measured DFT coefficients, providing insight into the numerical stability of the inversion. Numerical experiments demonstrate close agreement between the theoretical predictions and observed recovery thresholds over a broad range of problem parameters.
ER -