通过傅里叶表示进行时频分析
Time-Frequency analysis via the Fourier Representation
AI总结：
本文提出基于傅里叶变换的时频分析方法，通过频率域信号的相位获取时间信息，定义了频率导数的'频繁aneous时间'概念，用于非稳态信号和非线性系统的时频表示。
摘要：
非稳态信号和非线性系统需要时频表示。在时域信号中，频率信息来源于Gabor分析信号的相位，实际通过逆傅里叶变换获得。本文提出通过傅里叶变换将时域信号映射到频域的时频分析方法。在此研究中，我们从频域信号的相位获取时间信息，并获得时频表示。为了在傅里叶域中获取时间信息，我们定义了'频繁aneous时间'的概念，即相位的频率导数。这非常类似于群延迟，也定义为相位的频率导数，并且只有在正数时才有物理意义。频繁aneous时间总是正或负，取决于信号是否仅定义在正时间或负时间上。如果信号在正负时间上都定义，则将信号分为两部分，分别处理正时间和负时间。所提出的频繁aneous时间和基于傅里叶变换的时频分布仅包含傅里叶谱中存在的频率。在许多模拟数据和实际数据上的仿真和数值结果展示了所提出方法在信号时频分析中的有效性。
英文摘要：
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the inverse Fourier transform. This study presents time-frequency analysis by the Fourier transform which maps the time-domain signal into the frequency-domain. In this study, we derive the time information from the phase of the frequency-domain signal and obtain the time-frequency representation. In order to obtain the time information in Fourier domain, we define the concept of `frequentaneous time' which is frequency derivative of phase. This is very similar to the group delay, which is also defined as frequency derivative of phase and it provide physical meaning only when it is positive. The frequentaneous time is always positive or negative depending upon whether signal is defined for only positive or negative times, respectively. If a signal is defined for both positive and negative times, then we divide the signal into two parts, signal for positive times and signal for negative times. The proposed frequentaneous time and Fourier transform based time-frequency distribution contains only those frequencies which are present in the Fourier spectrum. Simulations and numerical results, on many simulated as well as read data, demonstrate the efficacy of the proposed method for the time-frequency analysis of a signal.
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