A spectral Doppler processor for an ultrasound system produces blood flow velocity estimates by processing a sequence of complex blood flow echo samples with an FFT algorithm. The FFT algorithm is executed with a long window of samples to produce velocity estimates with good velocity precision and is executed with a short window of samples to produce velocity estimates with good time precision. The long window algorithm is used when blood flow velocity is not changing rapidly, and the short window algorithm is used when blood flow velocity is changing rapidly.