Instantaneous frequency and time-frequency distributions
Instantaneous frequency and time-frequency distributions
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DOI：
10.1109/icassp.1995.480405
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发表时间：
1995-05
期刊：
影响因子：
--
通讯作者：
B. Tacer;P. Loughlin
中科院分区：
文献类型：
--
作者：
B. Tacer;P. Loughlin
一般认为，时频分布（TFD）的条件平均频率应该等于信号的瞬时频率。瞬时频率作为分析信号相位的导数的普遍接受的定义有时会导致奇怪的结果。虽然人们普遍认为，积极的TFD和满意的所谓的“瞬时频率约束”一般是不相容的，我们表明，人们总是可以找到一个复杂的信号，其中的真实的部分是给定的信号，其中的衍生物的相位是一致的边际和积极性。此外，对于所考虑的情况，该信号的相位的导数（其通过设计等于正TFD的条件平均频率）是瞬时频率的合理且易于解释的选择。
It is generally stated that the conditional mean frequency of a time-frequency distribution (TFD) should equal the instantaneous frequency of the signal. The commonly accepted definition of instantaneous frequency as the derivative of the phase of the analytic signal sometimes leads to curious results. Although it is commonly held that positivity of the TFD and satisfaction of the so-called "instantaneous frequency constraint" are generally incompatible, we show that one can always find a complex signal, the real part of which is the given signal, for which the derivative of the phase is consistent with the marginals and positivity. Furthermore, for the cases considered, the derivative of the phase of this signal, which by design equals the conditional mean frequency of a positive TFD, is a reasonable, readily interpretable choice for instantaneous frequency.