## 3 Experimental Setup and Results & Discussion
The blue curve in Figure 7b shows that the simultaneous measurement of the fiber attenuation, and the Fresnel reflection event in the FUT can be achieved by adding a DC component of the backscattered signal. However, the low-pass filter will reduce the signal-to-noise ratio of the reflected signal. What we hope to achieve is to improve its spatial resolution without reducing the dynamic range of the OTDR. The duration of the complementary D-LPM pulse we used was 4 us, so the pulse duration of the single-pulse OTDR is also 4 us. The red curve in the same figure represents the average results of 16384 experiments with a conventional OTDR system having a pulse width of 4 us, under the same experimental conditions. The 400-m  
Figure 5: Schematic block diagram of the digital linear frequency modulation (LFM)-based optical time domain reflectometry. FP-LD: Fabry–Perot (FP) laser diode; FPGA: field-programmable gate array; APD: avalanche photodiode; FUT: fiber under test; ADC: analog-to-digital converter; DSP: digital signal processor. Figure 6: Periodic digital linear frequency modulation (LFM) signal. (**a**) Time-domain waveform, with a pulse period of 1.2 ms, (**b**) zoom-in of the digital LFM signal in (a), with a pulse width of 4 us and a sweep frequency ranging from 4 MHz to 8 MHz (\(B=4\) MHz). spatial resolution of the conventional OTDR is determined by the pulse width, since the pulse width is 4 us and the measurement time is only 19 s and we did not use any other curve fitting technique. The dynamic range of the single-pulse OTDR shown in Figure 7b is less than 20 dB. Figure 7b shows that, under the same conditions, the dynamic range of DLFM-OTDR is improved by 7 dB and the spatial resolution is improved by more than 10 times, compared to the conventional OTDR. As shown in Figure 7, when the STFrFT window is rectangular, there are a series of evident sidelobes around the high reflection peak in the reflection event measured. To suppress them, we use the Hamming window as the STFrFT window, and the results are shown in Figure 8. Figure 8a illustrates the measurement result when only the primary LFM signal in the backscattered signal is considered. A comparison with the results in Figure 7 suggests that the measured reflection event is mainly a high reflection peak with almost no sidelobes. However, the spatial resolution defined by the FWHM of the mainlobe is reduced by a factor of 1.6 to a width of 48 m, which is almost the same as the result in Figure 4b. Figure 8b shows the measurement results when considering the DC component as well. A comparison with the results in Figure 7b indicates that the dynamic range is still improved by 7 dB with respect to the conventional OTDR and there is no sidelobe in the reflection peak, but this broadens 1.6 times to reach 48 m. Therefore, using the Hamming window as the STFrFT window can significantly suppress the sidelobes in the reflection peaks but also widens the mainlobe. According to Equation (7), the digital LFM signal can be decomposed into a series of LFM signals with different sweep frequency ranges because the DLFM-OTDR spatial resolution is inversely proportional to the sweep frequency range. The spatial resolution can also be improved without affecting the dynamic range by extracting the higher-order LFM signal with a large sweep frequency range, that is, the tertiary or quinary LFM signal. Figure 9a shows the measurement results obtained by extracting the tertiary LFM signal; since its sweep frequency range is three times that of the primary LFM signal, the spatial resolution is enhanced by 10 times to 10 m. Figure 9b shows the results for the addition of the corresponding DC component; although the dynamic range is not affected, the spatial resolution of the reflection event sharply deteriorates. Since the intensity of the tertiary LFM signal is relatively weak, it is easily covered by the DC component, affecting the spatial resolution of the reflection event. Figure 7: Measurement results of the rectangular short-time fractional Fourier transform window.