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Iterative reconstruction of speech from short-time Fourier transform phase and magnitude spectra

机译：短时傅立叶变换相位和幅度谱的语音迭代重建

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摘要

In this paper, we consider the topic of iterative, one dimensional, signal reconstruction (specifically speech signals) from the magnitude spectrum and the phase spectrum. While this topic has been extensively researched and documented, we wish to recast some well-established results for the benefit of new researchers and those who desire a short, yet comprehensive, review of the subject. The three main points of the review are: (ⅰ) a signal can be reconstructed to within a scale factor from its phase spectrum, (ⅱ) a signal cannot be reconstructed to within a scale factor from its magnitude spectrum, and (ⅲ) a signal can be reconstructed to within a scale factor from its magnitude spectrum when the phase-sign (i.e., one bit of phase spectrum information) is known. Through a number of illustrative examples, we first demonstrate how the algorithms work when the spectral information is determined over the entire duration of the signal. We then demonstrate that the algorithms are equally valid for reconstruction of a signal from the spectra obtained from short-time segments. In addition, we present the results of some further experimentation in which we have attempted to reconstruct a speech signal from only partial phase spectrum information (in the absence of all magnitude spectrum information). We make the following observations: (ⅰ) intelligible signal reconstruction (albeit noisy) is possible from knowledge of only the phase spectrum sign information, (ⅱ) an intelligible signal cannot be reconstructed from knowledge of only the phase spectrum frequency-derivative or only the phase spectrum time-derivative, and (ⅲ) an intelligible signal can be reconstructed from the combined knowledge of both the phase spectrum frequency-derivative and time-derivative.
机译：在本文中，我们考虑了基于幅度谱和相位谱的一维迭代信号重建（特别是语音信号）的主题。尽管对该主题进行了广泛的研究和记录，但我们还是希望重现一些公认的结果，以利于新的研究人员以及希望对该主题进行简短而全面的审查的人员。审查的三个主要方面是：（ⅰ）信号可以从其相位谱重构到比例因子之内；（ⅱ）信号不能从其幅度谱重构到比例因子之内；和（ⅲ）a当已知相位符号（即一位相位频谱信息）时，可以从其幅度频谱将信号重构到比例因子之内。通过许多说明性示例，我们首先演示了在整个信号持续时间内确定频谱信息时算法如何工作。然后，我们证明算法对于从短时间段获得的频谱重构信号同样有效。另外，我们提出了一些进一步实验的结果，在这些实验中，我们试图仅从部分相位频谱信息（在没有所有幅度频谱信息的情况下）重构语音信号。我们进行以下观察：（ⅰ）仅从相位频谱符号信息的知识就可以进行可理解的信号重建（尽管有噪声），（ⅱ）仅从相位频谱频率导数或仅通过频谱的知识就不能重建可理解的信号可以从相位频谱频率导数和时间导数的组合知识中重建相位频谱时间导数和（ⅲ）可理解的信号。

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