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The performance of many signal-processing applications in ultrasound medical imaging, including elastography, blood flow imaging, tissue velocity imaging, and acoustic radiation force impulse imaging, depends on the performance of their time-delay estimators. In this paper, we present a new time-delay estimator based on the tracking of individual samples using a continuous representation of the echo signal. We also present the use of the same interpolation approach to improve the performance of the zero-crossing tracking delay estimator. Simulation results show that sample tracking algorithms significantly outperform commonly used window-based algorithms in terms of bias and standard deviation. Sample tracking algorithms also have higher sensitivity and resolution compared with traditional delay estimators, including recently introduced spline-based continuous time-delay estimators, because they provide the displacement of individual samples. Experimental results demonstrating the viability of sample tracking delay estimation are also presented.