Real-time BAPES implementation for fast spectral Doppler estimation

The echoes backscattered from blood red cells moving in a vessel are typically elaborated though a spectral analysis and then displayed in the sonogram. The preferred frequency estimator is the Welch method, which is robust and fast, but requires at least 64-128 samples, gathered one per pulse repetition interval (PRIs), to guarantee adequate spectral resolution. The Blood Amplitude and Phase EStimator (BAPES) is an alternative technique that was recently proven suitable for producing good spectrograms using down to 16 PRIs per frame. This achievement allows a better time resolution and/or higher B-mode frame rates when working in Duplex mode, but unfortunately BAPES requires much more calculations than Welch, making its real-time employment quite challenging. In this work we present a BAPES implementation on a state-of-the-art fixed point DSP. This implementation, exploiting the Newton method for inverse matrix approximation, produces a 128 frequency-point frame in less than 5 ms. The error measured in a test on the common carotid artery of a volunteer was lower than 0.2% with respect to a floating-point reference implementation.