Comparison between the methods of the norm L1, L2, hilbert transform and phase analysis to obtain the time of flight of ultrasonic signals

Abstract

Some techniques to estimate the time of flight (TOF) allow getting a larger resolution, more than a sampling period. Therefore, it is possible to obtain a greater accuracy in the measurement of acoustic parameters using the TOF.

In this work a comparison between the mentioned methods is carried out; analyzing the standard deviation of the time of flight in relation to the sign to noise ratio (SNR) between 5 dB to 40 dB and a bandwidth of 4 MHz, 5 MHz and 6 MHz to -6 dB of simulated ultrasound signals, with the purpose of analyzing the performance of each method.

The results demonstrate that the method of the phase estimation presents the bigger values of standard deviation. For high-SNRs the methods of the L1 and L2 norm present similar values; furthermore, they exhibit the lowest values of standard deviation of the TOF estimation of the four methods. Finally, it was observed that for low SNR the method of Hilbert transform allows to obtain values of standard deviation similar to the methods of the norm L1 and L2 with a smaller time of processing of the signal.