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首页> 外文会议>5th International Symposium on Test and Measurement (ISTM/2003) Vol.3 Jun 1-5, 2003 Shenzhen, China >Estimating the Instantaneous Frequency of a Signal
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Estimating the Instantaneous Frequency of a Signal

机译：估计信号的瞬时频率

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摘要

The frequency of a sinusoidal signal is a well defined quantity. However, often in practice, signals are not truly sinusoidal, or even aggregates of sinusoidal components. Nonstationary signals in particular do not lend themselves well to decomposition into sinusoidal components. For such signals, the notion of frequency loses its effectiveness, and one needs to use a parameter which accounts for the time-varying nature of the process. This need has given rise to the idea of instantaneous frequency (IF). The instantaneous frequency of a signal is a parameter which is often of significant practical importance. In many situations such as seismic, radar, sonar, communications, automation, vibration engineering, and biomedical applications, the instantaneous frequency is a good descriptor of some physical phenomenon. In this paper, the basic concepts necessary for the interpretation and use of the instantaneous frequency of a signal are investigated, and the definition of instantaneous frequency is discussed. A method for analyzing non-stationary signal is introduced to calculate instantaneous frequency of a signal, and the estimation procedures for the instantaneous frequency are given. This method is based principally on the concept of the local wave decomposition, according to which any complicated set of data can be decomposed into a finite and often small number of intrinsic mode functions that admit well-behaved Hubert transforms. Since the decomposition is based on the local characteristic time scale of the data, it is applicable and have the advantage that their spectral characteristics can be accurately controlled in almost every regard including duration, bandwidth and energy. These signals are also used extensively for estimation of Doppler frequency shift in radar returns, and for tracking the narrow-band components of passive sonar. They also appear in various natural situations, such as in the echo-location systems of bats. For these signals, the IF is an important characteristic; it is a time-varying parameter which defines the location of the signal's spectral peak as it varies with time. Conceptually it may be interpreted as the frequency of a sine wave which locally fits the signal under analysis. Physically, it has meaning only for monocomponent signals, where there is only one frequency or a narrow range of frequencies varying as a function of time. For multicomponent signals, to nonlinear and non-stationary processes. With the Hilbert transform, the intrinsic mode functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The main innovations embodied in this method are the introduction of the intrinsic mode functions based on local properties of the signal, which make the instantaneous frequency meaningful. An example from simulation experiment is given to demonstrate the power of this method. The method can be used to analyze complicated non-stationary signal. At the end of this paper, some related problems are discussed.
机译：正弦信号的频率是一个明确定义的量。但是，在实践中，信号通常不是真正的正弦波，甚至不是正弦波分量的集合。非平稳信号尤其不能很好地分解成正弦分量。对于这样的信号，频率的概念失去了效力，人们需要使用一个说明过程时变性质的参数。这种需求引起了瞬时频率（IF）的想法。信号的瞬时频率通常是非常重要的参数。在地震，雷达，声纳，通信，自动化，振动工程和生物医学应用等许多情况下，瞬时频率可以很好地描述某些物理现象。在本文中，研究了解释和使用信号瞬时频率所需的基本概念，并讨论了瞬时频率的定义。介绍了一种分析非平稳信号的方法来计算信号的瞬时频率，并给出了瞬时频率的估计程序。此方法主要基于局部波分解的概念，根据该概念，任何复杂的数据集都可以分解为有限的且通常为少量的固有模式函数，这些函数可以接受行为良好的Hubert变换。由于分解是基于数据的本地特征时间尺度，因此它是适用的，并且具有可以在几乎所有方面（包括持续时间，带宽和能量）精确控制其频谱特征的优点。这些信号还广泛用于估算雷达回波中的多普勒频移，以及跟踪无源声纳的窄带分量。它们还出现在各种自然情况下，例如在蝙蝠的回声定位系统中。对于这些信号，中频是重要的特性。它是随时间变化的参数，用于定义随时间变化的信号频谱峰值的位置。从概念上讲，它可以解释为局部适合所分析信号的正弦波频率。从物理上讲，它仅对单分量信号有意义，在单分量信号中，只有一个频率或一小段频率随时间变化。对于多分量信号，适用于非线性和非平稳过程。利用希尔伯特变换，本征模式函数会产生瞬时频率作为时间的函数，从而可以清晰地识别出嵌入的结构。这种方法所体现的主要创新是基于信号的局部特性引入本征模式函数，这使瞬时频率变得有意义。通过仿真实验给出了一个实例，证明了该方法的有效性。该方法可用于分析复杂的非平稳信号。最后，讨论了一些相关的问题。

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