用新方法实现脉冲信号的瞬时谱分析，可看清肺部异常声音的时频结构。
Instantaneous Spectra Analysis of Pulse Series -- Application to Lung Sounds with Abnormalities
- 以线性外推代替周期边界条件，突破傅里叶分析的时频分辨率限制
- 成功解析出干啰音、哮鸣音及正常呼吸音的单个脉冲频谱与序列谱图
- 适合研究生物信号中非平稳脉冲特征，如肺部听诊异常分析
傅里叶分析的理论时间-频率分辨率极限源于其数值实现中的周期边界条件（PBC），该假设已沿用百年。我们此前提出以线性外推条件（LXC）替代PBC，无需周期性假设，从而实现脉冲序列的瞬时谱分析，取代短时傅里叶变换（STFT）。本文将该方法应用于两类异常肺音（干啰音、哮鸣音）及正常肺音进行示范。其中干啰音含随机脉冲序列，每个脉冲的频谱可独立获取，通过拼接形成脉冲序列的时频谱图。结果清晰展示了给定脉冲序列的时频结构特征。
原文摘要 · Abstract (English)
The origin of the "theoretical limit of time-frequency resolution of Fourier analysis" is from its numerical implementation, especially from an assumption of "Periodic Boundary Condition (PBC)," which was introduced a century ago. We previously proposed to replace this condition with "Linear eXtrapolation Condition (LXC)," which does not require periodicity. This feature makes instantaneous spectra analysis of pulse series available, which replaces the short time Fourier transform (STFT). We applied the instantaneous spectra analysis to two lung sounds with abnormalities (crackles and wheezing) and to a normal lung sound, as a demonstration. Among them, crackles contains a random pulse series. The spectrum of each pulse is available, and the spectrogram of pulse series is available with assembling each spectrum. As a result, the time-frequency structure of given pulse series is visualized.
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