Highly accurate vibrometry and ranging are important topics in the industrialized economy. Wherever optical measurement technology fails due to its high prices and vulnerability within harsh environments, millimeter-wave (mmWave) radar technology is well suited. This article introduces a signal processing chain for ultrawideband frequency-modulated continuous-wave (FMCW) radar. It uses fast-time measurement to evaluate the instantaneous phase, thus allowing for spatially resolved sensing of multiple simultaneously vibrating radar targets, faster than the chirp rate. In order to accomplish this, a sophisticated error model and a calibration scheme were derived. We used three FMCW radar systems covering a broad range of the mmWave spectrum to demonstrate the signal processing approach. In contrast to the commonly used slow-time measurement principle, the highest detectable frequency was improved from 55 Hz to at least 16 kHz, which is the upper limit of the audio range. Up to 10 kHz could be measured with an underlying large-scale motion of 0.4 m/s, while the vibration displacement was at a minimum of 30 nm.

中文翻译：

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使用超宽带 FMCW 雷达系统的空间分辨快速时间振动测量

高精度测振和测距是工业化经济中的重要课题。在光学测量技术由于其高昂的价格和在恶劣环境中的脆弱性而失败时，毫米波 (mmWave) 雷达技术非常适合。本文介绍了超宽带调频连续波 (FMCW) 雷达的信号处理链。它使用快速时间测量来评估瞬时相位，从而允许对多个同时振动的雷达目标进行空间分辨感测，速度快于啁啾率。为了实现这一点，我们导出了复杂的误差模型和校准方案。我们使用了三个涵盖广泛毫米波频谱的 FMCW 雷达系统来演示信号处理方法。与常用的慢时间测量原理相反，最高可检测频率从 55 Hz 提高到至少 16 kHz，这是音频范围的上限。可以在 0.4 m/s 的潜在大尺度运动下测量高达 10 kHz 的频率，而振动位移最小为 30 nm。