Identity between two computed velocimetry methods

In conventional ultrasound Doppler systems, the velocity component along the beam axis is obtained from the observed frequency shift. We have proposed two methods that use pure linear procedures to measure all the components of an arbitrary flow vector. In the first method, the first step is a Fourier transform of the received signals in the direction of the transducer array. The second step is also a Fourier transform, but in the polar-axis directions. In the second method, the first step is again a Fourier transform, but in the direction of the time-axis. The second step is not a Fourier transform but a projection integration in the polar-axis direction. In this paper, the identity of these methods in velocity resolution is shown.