# A New Signal Processing Method for Time-of-Flight and Center Frequency Estimation
###### Abstract  
Ultrasonic signal processing methodologies use many signal parameters to be investigated, one of which is time-of-flight (ToF). There are many and various methods used to determine ToF, such as threshold detection, peak-based methods, cross-correlation, zero-crossing tracking algorithms, etc. The application of most of these methods becomes problematic when the background noise becomes high and the signal amplitude, frequency, or propagation velocity changes. In order to partially solve these problems, this paper proposes a new and simple method to determine the time-of-flight and center frequency of signals based on the use of zero-crossing times of filtered signals to calculate these parameters. Taking advantage of the idea that these zero-crossing times are concentrated around the maximum of the signal envelope, they were used as the time-of-flight of the signal. 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 sheet molding compound 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. ultrasonic signal processing; time-of-flight estimation; center frequency; noisy signal; Lamb wave 2025155721  
18 April 202513 May 202513 May 202519 May 202519 May 2025  
Ultrasonic signal processing methodologies use many signal parameters to be investigated (amplitude, phase, frequency, group propagation time), one of which is time-of-flight (ToF). There are many and various methods used to determine ToF, such as threshold detection [1; 2; 3], peak-based methods [4; 5; 6], cross-correlation [7; 8; 9; 10; 11], zero-crossing tracking algorithms [12; 13; 14], etc. Among these algorithms, the simplest is used to determine the propagation time of the signal based on a threshold of when the signal amplitude exceeds a set level [15]. However, due to the noise level in the signal and the attenuation of the signal, the use of the threshold method is sometimes compromised by the problems of multi-significance and uncertainty. The cross-correlation method has robustness to noise interference and is often used in ToF determination [8]. However, the disadvantage of this method is that the signal must be cross-correlated with the transmitted (reference) signal in order to calculate the ToF. Obtaining a reference signal is difficult in most cases, and the evaluation of the cross-correlation itself is complicated [10]. Zero-crossing algorithms are sensitive to noise, so this method can only be used in a high signal-to-noise ratio (SNR) regime [13]. Recently, time-frequency signal processing methods have become widely used to estimate signal time-of-flight. A new ToF estimation method based on the short-time Fourier transform (STFT) was proposed in [16]. In this method, the time and frequency components of the ultrasound signal are represented by the STFT, and their spectrum is projected into the time domain. The ToF is calculated from the location of the maximum modulus of the signal's STFT spectrum. The method has many advantages, but the estimation of ToF at signal-to-noise ratio SNR \(<8\) dB is problematic. A variety of wavelet-based algorithms, both continuous (CWT) and discrete (DWT) forms, are used to determine the propagation time of signals and reduce noise [17]. In [18], the measured signal was decomposed into a series of narrowband signals using a wavelet transform, and matching pursuit (MP) was used to derive a sparse representation of the signal.