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Misconceptions about instantaneous frequency, and complex signal representations through pole-zero manipulations

机译：关于瞬时频率的误解，以及通过零极点操纵进行的复杂信号表示

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摘要

Instantaneous frequency is an important characteristic of time-varying or non-stationary signals. The definition and interpretation of instantaneous frequency have been the subject of discussion and debate for decades. The most common approach is due to Gabor, whereby a specific complex signal, called the analytic signal, is associated with a given real signal by inverting the spectrum of the real signal over only the positive frequency axis; the instantaneous frequency is then taken to be the derivative of the phase. Other approaches for associating a particular complex signal to a given real signal, and hence obtaining different instantaneous frequencies, have also been proposed. One way to define the associated complex signal / instantaneous frequency is by imposing physical constraints, which we discuss. We also discuss the common interpretation of instantaneous frequency as the average frequency at each time, and point out when this interpretation holds, which is not usually the case. This leads to the question of what is the "average frequency at each time?" The answer, coupled with physical constraints on the complex signal representation, leads to a quadrature-AM / FM signal model. Finally, we consider methods that manipulate the poles and zeros of the signal to obtain a complex representation.
机译：瞬时频率是时变或非平稳信号的重要特征。几十年来，瞬时频率的定义和解释一直是讨论和辩论的主题。最常见的方法是由于Gabor的缘故，在这种方法中，特定的复杂信号（称为分析信号）通过仅在正频率轴上反转实信号的频谱而与给定的实信号相关联。然后将瞬时频率取为相位的导数。还已经提出了用于将特定的复信号与给定的实信号相关联并因此获得不同的瞬时频率的其他方法。定义相关的复信号/瞬时频率的一种方法是施加物理约束，我们将对此进行讨论。我们还将瞬时频率的常见解释作为每次的平均频率进行讨论，并指出这种解释何时成立（通常不是这种情况）。这就带来了一个问题，即“每次平均频率”是多少？答案加上对复杂信号表示的物理限制，导致了正交AM / FM信号模型。最后，我们考虑操纵信号的极点和零点以获得复杂表示的方法。

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  • 来源
    《Automatic Target Recognition XXV》|2015年|947606.1-947606.10|共10页
  • 会议地点 Baltimore MD(US)
  • 作者

    Patrick J. Loughlin;

  • 作者单位

    University of Pittsburgh, 302 Benedum Hall, Pittsburgh, PA 15261, USA;

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  • 原文格式 PDF
  • 正文语种 eng
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