宽带信号的相位恢复
Phase retrieval for wide-band signals
摘要：
本文研究宽带信号的相位恢复问题。我们解决以下问题：给定f $\in$ L2（R）在L2（R，e ^{2c |x| dx}）中进行傅里叶变换，我们找到所有函数g $\in$ L2（R）在L2（R，e ^{2c |x| dx}）中进行傅里叶变换，使得|f（x）|=| g（x）|对于所有x个$\in$ R。为此，我们首先通过共形双射将问题转化为圆盘上Hardy空间中的函数，并利用内外因子分解。我们还考虑了同样的问题与额外的约束，涉及一些变换的f和g，并确定这些约束力的唯一性的解决方案。
英文摘要：
This study investigates the phase retrieval problem for wide-band signals. We solve the following problem: given f $\in$ L 2 (R) with Fourier transform in L 2 (R, e^{2c|x|} dx), we find all functions g $\in$ L 2 (R) with Fourier transform in L 2 (R, e^{2c|x| dx}), such that |f (x)| = |g(x)| for all x $\in$ R. To do so, we first translate the problem to functions in the Hardy spaces on the disc via a conformal bijection, and take advantage of the inner-outer factorization. We also consider the same problem with additional constraints involving some transforms of f and g, and determine if these constraints force uniqueness of the solution.
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