Fig. 1. Schematic diagram of system modulation principle. (a) Conventional single-pulse modulation and (b) results; (c) frequency division multiplexing (FDM) modulation and (d) results

Fig. 2. FDM Φ-OTDR system setup and implementation principle

Fig. 3. Phase restoration method for FDM Φ-OTDR system

Fig. 4. Fundamental of SVD method

Fig. 5. Principle of threshold selection for improved SVD method. (a) Spectral difference results, with inset showing magnified view; (b) singular value matrix

Fig. 6. RBS intensity traces. (a) Before splice alignment; (b) after splice alignment

Fig. 7. Phase restoration results of vibration with different repetition rates. (a)(b) 5 kHz; (c)(d) 10 kHz; (e)(f) 25 kHz

Fig. 8. Results of sound signals restoration. (a) Sound signal phase reduction results; (b) 2D time-frequency map

Fig. 9. Denoising results of non-smooth sound signals. (a) Denoised sound signal; (b) 2D time-frequency plot; (c) frequency domain plot

Fig. 10. Discharge signal of 10 kV cable along surface

Fig. 11. Hankel matrix of discharge signal along surface, with inset showing magnified view

Fig. 12. Frequency difference results of surface discharge signal. (a) before elimination of periodic narrowband noise; (b) after elimination of periodic narrowband noise

Fig. 13. Surface discharge signals to eliminate noise. (a) Time domain waveform and denoising results of surface discharge signal; (b) spectral difference result before denoising; (c) spectral difference result after denoising