Ultrasonic Time Delay Difference Estimation With Analytic Signals and a Model System

In this brief, we present an approach for the subsample time delay difference estimation (TDDE) of two narrowband ultrasonic signals. TDDE with an accuracy in the low picosecond range and a low computational cost is essential to extend the application of compact ultrasonic clamp-on flow meters to flow velocities below 50 mm/s. A digitized sinusoidal measurement signal of an ultrasonic flow meter is transformed into an analytic signal by using a time-discrete Hilbert transform. The phase shift between two analytic signals is proportional to the time delay difference of the two ultrasonic waves. In our approach, the response of the measurement system is compared with that of a model system. The standard error for the TDDE is 5 ps for a sampling time of 100 ns without interpolation under typical operating conditions. The time delay difference is calculated with tight tolerances, paving the way to the measurement of the smallest volume flows with high accuracy.