Baseband velocity estimation for second-harmonic signals exploiting the invariance of the Doppler equation

All Doppler systems, whether conventional Doppler domain or radio frequency (RF) processing is employed, relate the temporal frequency characteristics of the signal at a certain point in depth as function of time to the spatial frequency characteristics of the received signal as function of depth. The mean frequency of the latter may change as a result of depth-dependent attenuation, nonlinear scattering mechanisms, as in harmonic imaging of ultrasound contrast agents, or RF signal demodulation. For all these cases, the relationship between spatial and temporal mean frequency and target velocity is still governed by the familiar Doppler expression if the signal modifications have been properly accounted for. A major drawback of RF signal processing to extract the target velocity is the large number of data points to consider. The computational complexity increases further for harmonic imaging. It is shown conceptually, and demonstrated by signal simulations, that prior to velocity estimation RF demodulation followed by decimation (1) does not affect the Doppler equation, (2) enhances the information content of the samples, (3) reduces the computational load by a factor of four and for harmonic signals by a higher factor, and (4) while demodulation does not have to be actually performed, but can be accounted for by a scaling factor in the cross-correlation function. It is concluded that decimation hardly affects the precision of the velocity estimate if possible frequency aliasing is maintained within bounds, suggesting that the decimation factor is not critical.