An innovative application of the Hilbert transform to time delay estimation of overlapped ultrasonic echoes

In many areas, the estimation of time delay between two received signals is desired. An innovative process is proposed based on using the Hilbert transform of the impulse response evaluated from the two signals. A pure delay is thus transformed in a hyperbola whose vertical asymptote is located at a time yielding to the unknown shift in time. The precision, and resolution in overlapping are investigated from simulated signals. The measurement is also studied for an impulse response differing from the delta function. It is then demonstrated that when dispersive effects are sensitive, the technique leads to the asymptotic low frequency value of the phase delay. From the point of view of ultrasonic applications, these advantages are illustrated in comparison with classical input-output cross-correlation.