In this paper, we focus on the approximation of smooth functions $f: [-\pi, \pi] \rightarrow \mathbb{C}$, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram) measurements. Two algorithms are developed for approximately inverting such measurements, each with theoretical error guarantees establishing their correctness. A detailed numerical study also demonstrates that both algorithms work well in practice and have good numerical convergence behavior.

翻译：在本文中,我们侧重于光滑函数的近似值$f:[-\pi,\pi]\rightrow \mathbb{C}$,直到无法解决的全球阶段的模糊度,从一套短时Fourier变换(即光谱图)等值(STFT)的有限量测。为大致颠倒这种测量而开发了两种算法,每种算法都有理论错误保证其正确性。详细的数字研究还表明,两种算法在实践中运作良好,数字趋同行为良好。