The Doppler return (in your carotid artery ultrasound) is your 4 MHz signal frequency-modulated by the velocity shift. I would use the signal processing toolbox demod function, modeling the signal as frequency-modulated with a 4 Mhz carrier. You can then do the calculations to use the demodulated output to calculate velocity. (I would do a fft on the original signal to confirm first the bandwidth and other characteristics of the signal.)
I’ve not done that myself, so you may have to look through the literature in PubMed to find the appropriate equations. You are not the first person to do this, so there should be biomedical engineering literature references, if not also textbook references.
