# A New Signal Processing Method for Time-of-Flight and Center Frequency Estimation
## 4 Discussion and Conclusions  
This article proposes a simplified approach to determine the time-of-flight (ToF) of signals based on the use of zero-crossing times of filtered signals to calculate these parameters. Together with the ToF, the center frequency of the signal was also determined. The proposed method was adapted to the processing of experimental signals obtained during various ultrasound investigations. By processing S\({}_{0}\) mode signals propagating in the SMC plate, the propagation velocity of this mode was calculated. Its value was compared with the value obtained by the 2D FFT method. The obtained results differed by 0.9%. Using simulated signals propagating in 1 mm-thick aluminum, the phase and group velocity segments of the A\({}_{0}\) mode were calculated. Their values differed by 0.7% from the theoretically calculated values of the dispersion curves by the SAFE method.  
The results obtained during these investigations confirmed the effectiveness of the method and highlighted its advantages in comparison with other methods. Unlike threshold and peak-based methods, uncertainties due to the noise level in the signal are avoided. No threshold for signal capture is required. It is suitable for signals with a reasonably low signal-to-noise ratio. Compared to the correlation method, there is no need to have a reference signal. As an additional parameter, the center frequency of the signal was set. In the proposed method, all signal processing procedures can take place in an automated mode, depending on the signal's frequency response, by selecting the bandwidths of the filters. This enables the use of the method in automated measurements.  
However, this method has some limitations in terms of the signal processing algorithm. The overlap of multiple signals limits the application of the method, as the absence of envelopes for individual signals does not provide the ability to separate those signals. In the case of a low signal-to-noise ratio, the frequency characteristic of the signal can no longer be distinguished automatically. This can be done manually, and further processing of the signals was not affected in this case.  
However, the discussed shortcomings do not diminish the possibilities of applying this signal processing method for processing both ultrasonic and acoustic signals.  
Figure 9: Segments of phase and group velocities calculated using the proposed methodology (dots) and dispersion curves calculated using the SAFE method (lines).  
**Funding:** This research was funded by the Research Foundation of the Research Council of Lithuania under the project \"COMMET\". A combined signal processing method for determining the location and size of defects using higher-order Ultrasound Guided Waves, No. MIP-23-119.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The author declares no conflicts of interest.