# Why is there a Nyquist limit in pulsed-wave doppler ultrasound?

The Nyquist limit represents the maximum Doppler shift frequency that can be correctly measured without resulting in aliasing, and always equals the Pulse Repetition Frequency (PRF)$$/2$$.

However why is this relevant for Pulsed-wave ultrasound? If I understood correctly, if a pulse is send out, reflected on a moving object, and received, the speed can be calculated using Dopplers formula $$v=(c\,\Delta d)/(2f_{0}\cos\alpha)$$. If you increase or decrease the PRF, you just get more or less velocity measurements per second, so why does aliasing or the Nyquist limit exist in this case?

I get when the region of interest is too deep, the wave takes longer to travel and PRF must be lowered to give the wave time to arrive, but this still does not explain why the ultrasound machine would be unable to calculate the correct velocity from the returned signal (or cause aliasing).

Imagine that you send out not N coherent (!) short pulses each of length $$T_p$$ with gap between the consecutive ones $$T_g$$ but a single long pulse of length $$T_N = N(T_p+T_g)$$. This is a single pure sinusoid pulse of length $$T_N$$; when you coherently detect it with the properly Doppler shifted local oscillator there is no Nyquist anti-aliasing effect, instead the detection results in a single sample whose squared modulus is proportional to the energy of the Doppler shifted long pulse. But when you detect the pulsed sequence each short pulse is individually sampled, and there will be N samples separated by $$T_0=T_p+T_g = \frac{1}{PRF}$$ and whose coherent combination then brings in the aliasing effect you have to worry about; you are just sampling a long sinusoid...