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摘要: 激光多普勒雷达实际测得的振动信号绝大多数都是时变信号，而基于傅立叶变换的时频分析方法是处理时变信号的有利工具。本文针对激光多普勒雷达测得的实际振动信号，比较了魏格纳-维利分布、平滑伪魏格纳-维利分布、频谱图、波恩-约旦分布和扩展修正B分布5种形式的时频分析性能。利用激光多普勒雷达测量实际单音响产生的啁啾信号振动、双音响产生的二分量啁啾信号振动、以及成年男性心跳振动3种振动，分析了时频图的分辨率和交叉项抑制情况，并通过计算时频聚集度指数，比较了5种分布情况下振动的分析性能。实验证明，扩展修正B分布的性能优于其他4种时频分布，扩展修正B分布更适合应用于激光多普勒雷达材料共振频率探测和心跳检测领域。Abstract: Most actual vibration signals measured by lidar are time-varying signals. Methods of time-frequency analysis based on Fourier transforms are effective tools for processing time-varying signals. In this paper, the properties of the Wigner-Wiley distribution, the smooth pseudo-Wigner-Wiley distribution, the spectrogram, the Bonn-Jordan distribution, and the extended modified B distribution are compared and analyzed with actual vibration signals measured by laser Doppler radar. Three kinds of vibrations are measured with a laser Doppler radar: chirps generated by a single loudspeaker, two-component chirps generated by two loudspeakers, and adult male heartbeat vibrations. Their time-frequency distribution resolution and the suppression of cross-terms are analyzed. By calculating the time-frequency concentration index, the analysis capacites of the five distributions for three vibrations are compared. Experimental results indicate that the performance of the extended modified B distribution is better than that of the other four time-frequency distributions. Therefore, the extended modified B distribution is more suitable for the detection of material resonance frequency of laser Doppler radar and the detection of heartbeat.
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图 3 双声光调制相干激光多普勒雷达原理图
Figure 3. Block diagram of coherent laser Doppler radar with double acoustic optic modulation
图 4 双声光调制相干激光多普勒雷达实验装置图
Figure 4. Experimental device of coherent laser Doppler radar with double acoustic optic modulation
图 5 单分量啁啾信号的振动时域图及其时频分布
Figure 5. Time domain and time frequency distribution of single component chirps
图 6 二分量啁啾信号振动时域图及其时频分布
Figure 6. Time domain and time frequency distribution of two component chirps vibration
图 8 成年男性心跳振动时频分布
Figure 8. Time frequency distribution of adult male heatbeat vibration
表 1 单分量啁啾信号的振动时频聚集度评价
Table 1. Evaluation of time frequency concentration of single component chirps vibration
时频分布 WVD SPWVD SPEC BJD EMBD 评价指数 1.89×10−4 5.05×10−5 2.88×10−5 1.97×10−4 2.12×10−4 
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表 2 二分量啁啾信号振动时频聚集度评价
Table 2. Evaluation of time frequency concentration of two component chirp vibration
时频分布 WVD SPWVD SPEC BJD EMBD 评价指数 8.88×10−5 7.12×10−5 1.04×10−5 9.16×10−5 1.08×10−4
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表 3 成年男性心跳振动时频聚集度评价
Table 3. Evaluation of time frequency concentration of adult male heatbeat vibration
时频分布 WVD SPWVD SPEC BJD EMBD 评价指数 2.67×10−4 3.07×10−4 4.00×10−4 4.94×10−4 5.56×10−4
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