发表机构
School of Mathematical Sciences; LPMC, Nankai University（数学科学学院; 南开大学，理论力学与应用力学教育部重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对多窗口STFT相位恢复，提出基于Shannon插值和解析平方根提取的双窗口算法，并引入第三窗口和K-符号方法解决全局符号不稳定，适配SCR算法，理论证明稳定性并实验验证有效性。
AI 中文摘要
短时傅里叶变换（STFT）相位恢复旨在从频谱图幅度中重建信号。虽然理论上两个紧支撑窗口可保证唯一性，但完整的算法框架仍然缺失。本文系统地构建了多窗口STFT相位恢复的数值方案。理论上，我们为单窗口情形提供了一个非唯一性反例。然后，我们提出了一种基于Shannon插值和解析平方根提取的双窗口重建算法。为克服全局符号选择的不稳定性，我们引入第三个窗口和一种稳健的$K$-符号方法，该方法在局部确定符号。我们还将SCR算法适配到STFT设置中。对于$K$-符号方法，我们在有限的连续频率样本块上建立了确定性稳定性，误差界中明确包含了互补尾部的贡献。数值实验验证了所有方案的有效性。
英文摘要
STFT phase retrieval aims to reconstruct a signal from spectrogram magnitudes. While two compactly supported windows theoretically guarantee uniqueness, a complete algorithmic framework remains lacking. This paper systematically constructs numerical schemes for multi-window STFT phase retrieval. We theoretically provide a nonuniqueness counterexample for the single-window case. We then propose a two-window reconstruction algorithm based on Shannon interpolation and analytic square-root extraction. To overcome the instability of the global sign choice, we introduce a third window and a robust $K$-sign method that determines the sign locally. We also adapt SCR algorithm to the STFT setting. For the $K$-sign method, we establish deterministic stability on a finite contiguous block of frequency samples, with the contribution of the complementary tail explicitly included in the error bound. Numerical experiments validate the effectiveness of all schemes.
Comments32 pages
