Research Report on Noise-Shaped One-Bit Coefficients in Discrete Polynomial Fourier Extension

arXiv:2607.24868v1 Announce Type: new Abstract: This report studies noise-shaped one-bit coefficients in normalized discrete polynomial Fourier extension. For first-order Sigma-Delta quantization, the error is written as $e_k=u_k-q_k=\Delta v_k$ with a uniformly bounded state. Discrete summation by parts then yields variation estimates for complex weights and an $O(N^{-1})$ approximation rate on compact parameter sets. For the parabolic phase $\phi_{x,t}(\xi)=x\xi+t\xi^2$, the bound is expressed...