# Enhancement of Ultrasonic Guided Wave Signals Using a Split-Spectrum Processing Method
## 3 Signal Analysis
### Signal Synthesis  
The signal synthesis was utilised to generate the propagation of the dispersive wave modes in time/space, based on applying a frequency-dependent phase shift to the wave packet of interest via DISPERSE software (developed by Imperial College, London, UK) [30]. The core concept of this section was to identify the limitation of SSP in terms of finding the smallest defect size that could be detected, and to find the distance limitation when the location of the defect is close to a dominant feature with a high amplitude, such as a weld. In order to achieve that, the axisymmetric T(0,1) wave mode is excited with a 10-cycle pulse and a centre frequency of 44 kHz, using the synthesised model. It is assumed that there are only two reflection echoes (i) from the defect, and (ii) from the pipe's end. Since the proposed method has already proved its capability to remove the DWM [26], here, it is assumed that only the T(0,1) wave mode is reflected from the features on the pipe. According to [PERSON] et al. [31], there is a linear relationship between the amplitude of the reflected signal of T(0,1) and the cross-section area (CSA) of its defect. Hence, the attenuation of T(0,1) is linear, which means that if 10% of the excited signal reflects from the defect, then the rest of the energy (90%) will reflect from the pipe end. The set-up of this experiment is shown in Figure 4. The distances of the defect and pipe end are X = 3 m and X = 4.5 m from the excitation point, respectively. It is assumed that the defect reflects 6% of the total energy and rest of the energy (94%) is reflected by the pipe end, as displayed in Figure 5a. The reflections from the defect were reduced gradually in order to find the smallest defect size that can be recognised by the proposed method. These are illustrated in Figure 5, where the defect sizes are gradually reduced from 6% CSA to 1% CSA. The results demonstrate that the proposed method has the potential to detect defects down to 1% CSA when the distance between two features is 1.5 m. Then, in order to find the distance limitation, it is assumed that a 10% CSA defect is 1 m from the pipe end and it is moved towards the pipe end in steps of 0.1 m as illustrated in Figure 4. Results in Figure 6a-d clearly demonstrate that the defect was recognisable until the distance from the pipe end was around 0.7 m. After that, as shown in Figure 6f, the resolution was gradually reduced until it reaches 0.5 m. Afterwards, the defect reflection started to superimpose on the pipe end reflection, and it travelled below the limit of the resolution. Therefore, according to this result, SSP with the proposed parameters can detect small amplitudes that are close to the dominant amplitude only when the distance between them is greater than 0.5 m. Note that this is the result for 10 cycles of excitation signal with a defect size of 10% CSA and a centre frequency of 50 kHz. Figure 4: Synthesised setup for an eight inch pipe with a wall thickness of 8.179 mm and an outside diameter of 219.08 mm. Figure 5: Results for the synthesised signal before and after applying SSP ((polarity thresholding & Polarity thresholding with minimisation)PT & PTM). The defect and the pipe end are located at X = 3 m and X = 4.5 m from the excitation signal. The defect sizes are (**a**) 6% cross-section area (CSA); (**b**) 4% CSA; (**c**) 2% CSA; and (**d**) 1% CSA. Figure 6: _Cont._  
Furthermore, as shown in Figure 6, the results of PT and PTM algorithms are almost identical while the distance between the two peaks is greater than 0.8 m. However, the PT algorithm gives a better temporal resolution when the distance is around 0.5 m (Figure 5f). In these regions, the PT identify defects partially, whereas the PTM loses the information completely, and finally, when the distance is less than 0.4 m, both algorithms miss the defect.