A binary vector of length $N$ has elements that are either 0 or 1. We investigate the question whether and how a known can be reconstructed from limited set its discrete Fourier transform (DFT) coefficients. priori information is provides powerful constraint. prove uniquely defined by two complex DFT coefficients (zeroth, which gives popcount, first) if prime. If prime factors, additional must ...

In this work, we present two parallel algorithms for the large-scale discrete Fourier transform (DFT) on Tensor Processing Unit (TPU) clusters. The are associated with DFT formulations: one formulation, denoted as KDFT, is based Kronecker product; other famous Cooley-Tukey algorithm and phase adjustment, FFT. Both KDFT FFT formulations take full advantage of TPU's strength in matrix multiplicat...