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 guarantee 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 characterizes the stability of the inversion algorithms, as the lattice parameters are closely related to the required measurement precision. Numerical experiments demonstrate close agreement between the theoretical predictions and observed recovery thresholds over a broad range of problem parameters.