## 3 Experiments and Results
Curve 3, which is represented by the yellow curve, displays the time-domain waveform of the signal in the 30-50 MHz frequency band after phase demodulation. Lastly, curve 4, which is represented by the purple curve, illustrates the time-domain waveform of the signal in the 45-65 MHz frequency band after phase demodulation. The results demonstrate sine waves with a frequency of 200 Hz in all cases, confirming the sensing system's ability to accurately capture all four frequency components of the vibration signal. The results shown in Figure 7a all indicate sine waves with a frequency of 200 Hz, confirming that this sensing system can accurately capture all four frequency components of the vibration signal. The amalgamated vibration waveform, which resulted from the sequential concatenation of phase-demodulated waveforms extracted from the 4 NLFM pulses, is visually represented in Figure 7b. Employing a fast Fourier transform (FFT) technique on the aforementioned vibration waveform, as showcased in Figure 7b, has enabled the derivation of the corresponding power spectrum, which is prominently depicted in Figure 7c. Within Figure 7c, a conspicuous peak is discernible at precisely 9.8 kHz, which is concomitant with the inherent frequency of the vibration signal, demonstrating an impressive SNR at approximately 40 dB. Figure 7b,c collectively underscore the capabilities of this sensing system, underpinned by its employment of OFDM. Notably, this system exhibits an unprecedented capacity for augmenting the frequency response range inherent to vibration signals. Moreover, the amalgamation of phase demodulation results from multiple  
Figure 7: (**a**) The time-domain waveforms of the four vibration signals after phase recovery for the four carriers; (**b**) the time-domain waveform graph of the synthesized vibration signal from four signals; (**c**) the power spectrum of the synthesized vibration signal from four signals. NLFM pulses validates its capacity to reconstruct high-frequency vibration waveforms with precision. In the context in which the subcarrier center frequencies exhibit a spacing equivalent to 0.75 times the sweep bandwidth, an experiment was conducted involving the application of a swept sine wave signal with specific parameters. This signal entailed a rise time of 20 ms, a fall time of 20 ms, a frequency range spanning 1-10 kHz, and an amplitude characterized by a peak-to-peak driving voltage of 0.5 Vpp. The subsequent phase-recovered time-domain signal has been thoughtfully depicted in Figure 8a, while the outcome of subjecting the time-domain signal to short-time Fourier transform (STFT) is meticulously presented in Figure 8b. These visual representations, denoted as Figure 8a,b, serve as empirical evidence affirming the capability of this sensing system. Employing FDM, this system effectively expands its frequency response range from the initial 1-2.5 kHz to a more comprehensive 1-10 kHz range, marking a substantial fourfold enhancement in comparison to traditional single-frequency pulse approaches. When the subcarrier center frequency spacing was 0.75 times the sweep bandwidth, a triangular wave with a frequency of 200 Hz and an amplitude of 5 Vpp was applied to PZT1, while a sine wave with a frequency of 4.8 kHz and an amplitude of 1 Vpp was applied to PZT2. The results of the motion differential are shown in Figure 9, with a localization SNR of approximately 8 dB. Figure 8: (**a**) Time-domain waveform of the vibration signal with a 1-10 kHz frequency sweep at a single position; (**b**) STFT (short-time Fourier transform) results of the vibration signal with a 1-10 kHz frequency sweep at a single position. Figure 9: The results of motion differential for fixed-frequency vibration signals at multiple locations when the subcarrier center frequency spacing is 0.75 times the sweep bandwidth. The vibration applied to PZT1 is depicted in Figure 10a in the time domain, with the corresponding power spectrum shown in Figure 10b, which exhibits an SNR of approximately 55 dB.