STATIONARY ECHO CANCELING IN VELOCITY ESTIMATION BY TIME-DOMAIN CROSS-CORRELATION

The application of stationary echo canceling to ultrasonic estimation of blood velocities using time-domain cross-correlation is investigated. Expressions are derived that show the influence from the echo canceler on the signals that enter the cross-correlation estimator. It is demonstrated that the filtration results in a velocity-dependent degradation of the signal-to-noise ratio. An analytic expression is given for the degradation for a realistic pulse. Due to the inherent nonlinear method of velocity estimation, it is most appropriate to state a probability of correct detection at low signal-to-noise ratios. This probability is influenced by signal-to-noise ratio, transducer bandwidth, center frequency, number of samples in the range gate, and number of A-lines employed in the estimation. Quantitative results calculated by a simple simulation program are given for the variation in probability from these parameters. An index reflecting the reliability of the estimate at hand must be calculated from the actual cross-correlation estimate, as the probability is influenced by velocity and signal-to-noise ratio. It is shown that such an index can be calculated by a simple formula and used in rejecting poor estimates or in displaying the reliability of the velocity estimated.