Bias and variance in the estimate of the Doppler frequency induced by a wall motion filter

In pulsed Doppler flowmeters, processing of the Doppler signals is often done digitally. The first step in the analysis of the echoes is the filtering which is needed to remove stationary components and low frequency shifts induced by wall motion. This preliminary step is of utmost importance. The influence of uncorrelated noise on the measurement of Doppler signals at the input of this filter is analysed. The frequencies of the Doppler signals are extracted by an algorithm based on correlation techniques. We observed that the filter induces a correlated noise term, which results in an overestimation of the frequency. An effect similar to frequency aliasing may appear. The level of the bias is dependent on filter characteristics and noise level. Our study was carried out on simulated Doppler signals using first and second order filters. An especially desirable solution in flow mapping is proposed in order to decrease this error.